{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pyAudioKits.audio as ak"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The analysis of musical tones and noise in the previous section was done in the time domain. In this section we will introduce the concept of frequency domain and the way to analyze audio signals in it.\n",
    "\n",
    "# Fourier transform\n",
    "\n",
    "## Continuous-time signal Fourier transform\n",
    "\n",
    "We say that the continuous time period signal can be expanded into a fundamental wave of frequency $\\omega_0$ and harmonics of frequency $(k+1)\\omega_0 (k=1,2,...) $. This means that not only can we use the original $x(t)$ to represent a continuous time period signal, but we can use the frequency and amplitude to represent a continuous time period signal as long as we know the frequency and amplitude of the fundamental and harmonics. Thus, we now assume that there is a frequency axis with an infinite number of **frequency points $\\omega$**, and we can try to map the original one-dimensional signal $x(t)$ on the time axis to the frequency axis as $X(j\\omega)$, completing the mapping from the time domain to the frequency domain.\n",
    "\n",
    "Using the least squares method to make the difference of energy between the time domain representation and the frequency domain representation minimized. The conclusion to reach this condition is: let the value of all frequency points be $a_k$ multiplied by $2\\pi$. Expressed as the **spectral density function**, we have $X(j\\omega)=\\displaystyle\\sum_{k=-∞}^∞2\\pi a_k\\delta(\\omega-k\\omega_0)$. It can be seen that **the spectral density function of a periodic signal is a linear superposition of discrete impulse functions**. This function can be reduced to a Fourier series representation in the time domain $x(t)=\\displaystyle\\sum_{k=-∞}^∞a_ ke^{jk\\omega_0t}$ by $x(t)=\\frac{1}{2\\pi}\\displaystyle\\int_{-∞}^∞X(j\\omega)e^{j\\omega t}d\\omega$. \n",
    "\n",
    "So can non-periodic signals be mapped to the frequency domain? The answer is yes. If **the fundamental frequency $\\omega_0$ is infinitely small, i.e., the fundamental period $T$ is infinitely large**, then the frequency domain properties of **any (periodic or not) signal** can be expressed, and at this point it is generalized from the Fourier series to Fourier transform: the fundamental frequency $\\omega_0$ is infinitely small, so $k\\omega_0$ is considered as a continuous value $\\omega$ , $X(j\\omega)=\\displaystyle\\int_{-∞}^∞x(t)e^{-j\\omega t}dt$. At this point, the **integrated equation** of the continuous-time Fourier transform is obtained as $x(t)=\\frac{1}{2\\pi}\\displaystyle\\int_{-∞}^∞X(j\\omega)e^{j\\omega t}d\\omega$, and the **analytical equation** is $X(j\\omega)=\\displaystyle\\int_{-∞}^∞x(t)e^{-j\\omega t}dt$. It can be seen that **the spectral density function of a nonperiodic signal is a continuous function**.\n",
    "\n",
    "When the **period of the continuous-time periodic signal gradually expands**, $\\omega_0$ gradually shrinks, and the **impulse function consisting of $X(j\\omega)$ becomes more and more dense**. When the **period is infinitely large**, $\\omega_0$ is infinitely small, and $X(j\\omega)$** becomes a continuous function**, and the continuous-time non-periodic signal spectral density function is obtained.\n",
    "\n",
    "## Fourier transform of discrete-time signals\n",
    "\n",
    "But the signals we store in the computer are digital signals, that is, discrete-time signals, so how do they map to the frequency domain? \n",
    "\n",
    "Remember that the analog to digital signal (which in our case is also equivalent to the continuous time signal to the discrete time signal) uses a sampling operation. The signal is multiplied in the time domain by the impulsive string $p(t)=\\displaystyle\\sum_{n=-∞}^{+∞}\\delta(t-nT_s)$. The sampled time domain is represented as $x_s(t)=x(t)p(t)=\\displaystyle\\sum_{n=-∞}^{+∞}x(t)\\delta(t-nT_s)$ . The sampled frequency domain is represented as $X_s(j\\omega)=\\frac{1}{2\\pi}X(j\\omega)*P(j\\omega)=\\frac{1}{T_s}\\displaystyle\\sum_{k=-∞}^{+∞}X(j(\\omega-k\\omega_s))$ . We find that at this point **$X_s(j\\omega)$ is the result of a periodic extension of $X(j\\omega)$ on the spectrum with the sampling frequency as the base**. Its period is $\\omega_s=2\\pi/T_s$ and it contains all the spectral information in one period. At this point, the **integrated equation** of the Fourier transform of the discrete-time signal is obtained as $x[n]=\\frac{1}{2\\pi}\\displaystyle\\int_{\\frac{2\\pi}{T_s}}X(j\\omega)e^{j\\omega nT_s}d\\omega$, and the **analytical equation** is obtained as $X(j\\omega)=\\displaystyle \\sum_{n=-∞}^{+∞}x[n]e^{-j\\omega nT_s}$. \n",
    "\n",
    "By now the integrated and analytical equations are related to the sampling period $T_s$. To make them independent to $T_s$, we normalize the frequency domain by a factor $T_s$ (i.e., the inverse of the sampling rate), denoted as $X(e^ {j\\omega})=X(j\\omega T_s)$. Then we obtain the **integrated equation** for the Fourier transform of the discrete-time signal as $x[n]=\\frac{1}{2\\pi}\\displaystyle\\int_{2\\ pi}X(e^{j\\omega})e^{j\\omega n}d\\omega$, and the **analytic equation** is $X(e^{j\\omega})=\\displaystyle \\sum_{n=-∞}^{+∞}x[n]e^{-j\\omega n}$. In $X(e^{j\\omega})$, each $1 rad/s$ of $\\omega$ **actually represents the frequency** of $\\frac{1}{2\\pi T_s}Hz (\\frac{1}{T_s}rad/s)$. $X(e^{j\\omega})$ with $2\\pi$ as the period.\n",
    "\n",
    "## Discrete Fourier Transform\n",
    "\n",
    "Now the question comes up again, remember why we sampled the analog signal $x(t),-∞<t<∞$ into $x[n],0≤n<N_{max}$? This is because the computer cannot store the original analog signal, which is continuous and may still be infinite and non-causal. Then the spectral density function $X(e^{j\\omega}),-∞<\\omega<∞$ actually faces the same problem. We also need to perform some \"sampling\" operations on this spectral density function.\n",
    "\n",
    "Let the periodic impulse string $\\tilde p[n]=\\displaystyle\\sum_{r=-∞}^∞\\delta[n-rN]$, then we have $\\tilde x[n]=x[n]*\\tilde p[n]$, while $\\tilde X(e^{j\\omega})=X(e^{j\\omega})\\tilde P(e^{j\\omega})=X(e^{j\\omega})\\displaystyle\\sum_{k=-∞}^∞\\frac{2\\pi}{N}\\ delta(\\omega-\\frac{2\\pi k}{N})$, then we have $X[k]=X(e^{j\\omega})|_{\\omega=\\frac{2\\pi k}{N}}$, thus completing the sampling in the frequency domain. Using $W_N$ instead of $e^{-j\\frac{2\\pi}{N}}$ gives: \n",
    "\n",
    "$X[k]=\\displaystyle \\sum_{n=0}^{N-1} \\tilde x[n]e^{-jk(\\frac{2\\pi}{N})n}=\\sum_{n=0}^{N-1} \\tilde x[n]W_N^{kn}$​​​\n",
    "\n",
    "$\\tilde x[n]=\\frac{1}{2\\pi}\\displaystyle\\int_{2\\pi}X(e^{j\\omega})|_{\\omega=\\frac{2\\pi k}{N}}e^{j\\omega n}d\\omega=\\displaystyle\\frac{1}{N}\\displaystyle\\sum_{k=0}^{N-1} X[k]e^{jk(\\frac{2\\pi}{N})n}=\\frac{1}{N}\\displaystyle\\sum_{k=0}^{N-1} X[k]W_{N}^{-kn}$​\n",
    "\n",
    "And **time domain** with $N$ as the period for **periodic extension** becomes $\\tilde x[n]$. Instead of having $x[n]=\\begin{cases}x_d[n]\\quad 0≤n<N_{max}\\\\0\\quad others\\end{cases}$, we now have $\\displaystyle\\tilde x[n]=\\sum_{r=-∞}^∞x[n-rN]$. **The signal $\\tilde x[n]$ after the period extension may have a different frequency component than $x(t)$**.\n",
    "\n",
    "Originally in $X(e^{j\\omega})$, every $1 rad/s$ for $\\omega$ **actually represents the frequency** of $\\frac{1}{2\\pi T_s}Hz(\\frac{1}{T_s}rad/s)$. Now we have $\\tilde X[k]$ where each $k$ **actually represents** $\\frac{1}{T_sN}Hz(\\frac{2\\pi}{T_sN}rad/s)$ of the frequencies. Each k is said to be a **frequency point** in the spectrum, and the actual frequency represented is the **spectral resolution**. Sampling does not give a complete representation of the spectrum and in some cases misses frequency components in the spectrum, which is known as the **fence effect**. However, the time-frequency domain still satisfies the condition of energy equality, and the energy of the omitted frequency component is leaked to nearby frequency points, resulting in a new frequency component of the signal, which is known as **spectral leakage**.\n",
    "\n",
    "Remember that $X(e^{j\\omega})$ has a period of $\\frac{2\\pi}{T_s}$? This means that we only need to take $N$ consecutive frequency points in the spectrum to get all the information of the spectrum. Together with the fact that the spectrum of the real signal is symmetric about $\\omega=0$, we only need to take $N/2$ consecutive frequency points in the spectrum when we observe the spectrum, i.e. The spectrum is generally plotted by taking only $X[k],0≤k<\\frac{N}{2}$.\n",
    "\n",
    "Since $X[k]$ ar complex numbers, the spectrum is also divided into **amplitude spectrum** and **phase spectrum** as $|X[k]|$ and $\\angle X[k] (rad/s)$, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def periodicExtension(p,N): #Simulation of a function that performs 3 period extensions. p is the signal to be cycle extended, and N is the cycle extension period\n",
    "    L = 3 * N\n",
    "    p = ak.concatenate([ak.create_Single_Freq_Audio(0,0,p.sr,L/p.sr),p,ak.create_Single_Freq_Audio(0,0,p.sr,L/p.sr)])\n",
    "    p1 = p[0:L]\n",
    "    for i in range(N,len(p.samples)-L,N):\n",
    "        p1 = p1 + p[i:i+L]\n",
    "    return p1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pyAudioKits.analyse as aly\n",
    "\n",
    "p1 = ak.create_Single_Freq_Audio(0.1,8,256,1)   #Create a sine signal with an amplitude of 0.1, a frequency of 8Hz, a sampling rate of 256Hz and a duration of 1s\n",
    "p1.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DUj0j+B5wiOBZgpKklxyjmqoKDhzu4IkNO6MuRURyVKpnBMe5e2VaK8lRZ50wmfFj8qlb1cS5C6ZGXY6I5KBUzwjqzOz9g924mS0xs/VmttHMvn6U5T5sZm5m1YP9jUyXH49x/sKpPLimibaOrqjLEZEclGoQfA5YbmZvpHr7qJnFgZuAGmAhcJmZLexjuRKCkdD+PLjSs0dtVYL9rR08uUnNQyIy8lIKAncvIeh19BzggwRDV35wgNXOADa6+2Z3bwPuAi7uY7n/DdwAtKZYc9Y5e04ZJYV5untIRCKR6gNlfw08BiwHvhu+f3uA1aYR3HbabWs4L3m7i4EZ7n7fAL9/lZnVm1l9c3P23XNfmBfn/IVTeWDNdto71TwkIiMr1aaha4HTgVfd/b3AqQQd0Q2ZmcWAG4GvDLSsu9/i7tXuXl1eXn4sPztq1VRVsPdQO09v3hV1KSKSY1INglZ3bwUws0J3XwfMG2CdbcCMpOnpHNl1dQlQCTxqZq8QjHGwNBcvGAO8a24ZxQVx6lY1RV2KiOSYVINgq5lNAO4FHjSzPwCvDrDOs8BcM5ttZgXApcDS7i/dfZ+7l7n7LHefBTwNXOTu9YPch6xQlB/n3AVTuX91Ex1qHhKREZTqxeIPufted/8u8HfAT4G/GGCdDuAa4H5gLXC3u682s+vN7KJjqjpL1VYl2H2wjWde3h11KSKSQwY9Ioq7PzaIZeuAul7z+rzI7O7nDLaWbPOeE6cwJj9OXUMjZ80pi7ocEckRqTYNyQgYUxDnfQumsLxhO51d6t9PREaGgmCUqa2sYOeBw9S/ouYhERkZCoJR5px55RTlx1jWoLuHRGRkKAhGmeLCPM45cQrLGhrpUvOQiIwABcEoVFOVYPv+wzz32p6oSxGRHKAgGIXOXTCVovwYP/jTBj1TICJppyAYhcYV5nHdRYt4YuNObli+LupyRCTLDfo5AhkZl5w+k7WNLdz6Xy8zP1HKh0+bHnVJIpKldEYwin3zwgW8422T+cbvV/HClr1RlyMiWUpBMIrlx2P8+OOLmVpayGfvqGfH/pwdskFE0khBMMpNLC7g1suraWnt4LP/sYLW9s6oSxKRLKMgyADzE6Xc+LGTef61vXzr3gbc9XyBiAwfBUGGWFJZwbXnzuWeFVv5+ZOvRF2OiGQRBUEGufbcuVywaCrfq1vLExs00L2IDA8FQQaJxYz/87FTmFM+ji/86jle3XUw6pJEJAsoCDLMuMI8br28GjO48vZ6DhzuiLokEclwCoIMNHPyWG76q8Vsaj7I3/7mBXVOJyLHREGQoc6eU8a3LlzAg2u284OHNkRdjohkMHUxkcE+fdYs1ry+nx8+tIEFiRJqqiqiLklEMpDOCDKYmfH3H6rk1JkT+PLdL7K2cX/UJYlIBlIQZLjCvDg3f+I0xo/J58rb69l9sC3qkkQkwygIssCU0iJu/uRp7Gg5zOfvXEG7xjAQkUFQEGSJk2dM4IYPV/H05t38/R/XRF2OiGQQXSzOIh86dTprG1u45fHNLKgo5dIzZkZdkohkAJ0RZJn/uWQ+75pbxt/9oYH6V3ZHXY6IZAAFQZaJx4wfXbaY6RPHcvV/rOD1vW9EXZKIjHIKgiw0fmw+t15+Gq3tXVx1Rz1vtGkMAxHpn4IgS82ZUsK/XXoKq1/fz9d/t1JjGIhIvxQEWezcBVP56vvn8YcXXufmxzdHXY6IjFIKgiz3+XNO4AMnVXDD8nU8sm5H1OWIyCiU1iAwsyVmtt7MNprZ1/v4/stmtsbMVprZQ2Z2fDrryUVmxj995CQWJEr50l3Ps6n5QNQlicgok7YgMLM4cBNQAywELjOzhb0Wex6odveTgHuAf0pXPblsbEEet36qmoJ4jCt/Wc++N9qjLklERpF0nhGcAWx0983u3gbcBVycvIC7P+Luh8LJp4Hpaawnp02bMIaffOI0Xtt9iGvvep5OjWEgIqF0BsE0YEvS9NZwXn+uAJalsZ6cd8bsSVx38SIeXd/MP9+/PupyRGSUGBVdTJjZJ4Bq4D39fH8VcBXAzJnqNuFYfPztx7Pm9f38+2ObWFBRwsWnHC2bRSQXpPOMYBswI2l6ejjvCGZ2HvBN4CJ3P9zXhtz9Fnevdvfq8vLytBSbS77zwUWcMXsSX7tnJau27ou6HBGJWDqD4FlgrpnNNrMC4FJgafICZnYqcDNBCOjexhFSkBfjxx9fTNm4Qq66o54dLa1RlyQiEUpbELh7B3ANcD+wFrjb3Veb2fVmdlG42D8D44DfmtkLZra0n83JMCsbV8gtl5/GnkNtfO4/nuNwh7qhEMlVlmldD1RXV3t9fX3UZWSNP658nWt+9TyXnj6Df/jLKsws6pJEJA3MbIW7V/f13ai4WCzR+cBJx7G2cT83PbKJhceVcvk7ZkVdkoiMMHUxIXzl/Hmct2AK1/2/NTy1aVfU5YjICFMQCLGY8a+XnMLssmI+f+cKtuw+NPBKIpI1FAQCQElRPrdeXk1nl3Pl7fUcPNwRdUkiMkIUBNJjdlkx//evFvPS9ha++tsX6VI3FCI5QUEgR3jPieV8o2YByxqa+NEjG6MuR0RGgO4akrf463fNZm3jfm588CXmJUq4YFEi6pJEJI10RiBvYWZ8/y+rOHn6eL78mxdY39QSdUkikkYKAulTUX6cmz9ZzdjCPK68vZ69h9qiLklE0kRBIP1KjC/i5k+eRtO+Vq751fN0dHZFXZKIpIGCQI5q8cyJ/P2HKnli406+X7cu6nJEJA10sVgG9LHqGaxt3M/PnnyZBRUlfLR6xsAriUjG0BmBpOSbtQs4e85kvvn7Bp57bU/U5YjIMFIQSEry4jF+dNliEuOL+OwdK2japzEMRLKFgkBSNrG4gFsvr+bQ4Q4+e0c9re0aw0AkGygIZFDmJUq48ZJTeHHrPv7X71aRaeNZiMhbKQhk0C5YlOBvzzuR3z2/jZ8+8XLU5YjIMVIQyJB88X1zqKlM8P26tTz+UnPU5YjIMVAQyJDEYsa/fPRkTpxawjW/eo6Xdx6MuiQRGSKNWSzHZMvuQ1z0oyfIj8c4e04Z8xIlzJtawrxECRXjizQGssgooTGLJW1mTBrLTz99Oj98aANPbdrF75/f1vNdaVEe8xIlnDi1hPmJEuYlSpmXKGH8mPwIKxaR3nRGIMNq36F21m9vYX3TftY1tfDS9hbWNbXQ0vrmiGcV44uSwiF4zZkyjsK8eISVi2Q3nRHIiBk/Np8zZk/ijNmTeua5O437Wlnf1HJEODy1aRdtYUd28Zgxa/JY5odnDd1NTDMnjSUWU/OSSDopCCTtzIzjJozhuAljeO/8KT3z2zu7eGXnwfAMIgiHVdv2cd+qxp5lxuTHOXHquDAcSnuuP5SXFEaxKyJZSU1DMuocPNzBhh0HepqX1oevXQffHBNhcnHBEWcO3dciigv1bxuRvqhpSDJKcWEep8yYwCkzJhwxf+eBwz1nDuub9rN++wHuemYLbyR1dTFz0tgjwmF+ooTZZcXkxXWntEh/FASSMcrGFVI2p5Cz55T1zOvqcrbsORRce2hqYV3YzPTwuh10dgVnuwXxGCdMGce8qeOYlyhlfti0VFKUR0lRPuMK8yjIU1BI7lIQSEaLxYzjJxdz/ORiLliU6Jnf2t7JpuYDPRem1ze18OeXd3PvC6/3uZ3CvBglRfmUFuUxrigvCInCfEp6poPvSoryGBfOf/MVTI/Jj+u5CclICgLJSkX5cRYdN55Fx40/Yv6+N9rZsD243tDS2sGB1nZaWjtoOdwRvHdPt7bT3HI4/NzBgcMd/fzSm+IxY1zhkeFQ0mv6qKFSmM+4ojziuktKRpiCQHLK+DH5VM+aNPCCvXR2OQfbjgyLA60d7O8Jjg4OHH7zc/cyjftaeWlHOwfC+R1dA9+cUVwQD5qsesIij/x4jIJ4jPy84L0gz4LpeIyCvDffg3lGQV48fO9e/shlC4+YtqR1g3l5MdPZTQ5REIikIB4zSovyKS3KB8YMaRvuTmt7VxASh1MPlQOHO2jv7KKto4v2Tqeto4u2nunu1/De/WdGT/gkh0XyvLcGURBO8ViMeCz4bxYz63nPi4WfY0bcgveeeWbEY/Qsn9druXg4P37E8m+ukxeLEYvRs1z3tmP21nWO3DYYRsyC25xjFkxbuF0jfLfgv8lbls2SsExrEJjZEuDfgDhwm7v/Y6/vC4HbgdOAXcAl7v5KOmsSiYqZMaYgzpiCOFMGXnxQurqc9q4jw6K9s4vD4Xtb0ntb55HL9A6WnnU7u2jv8D7mdW8jmH/ojc4j1u3s8uDlTlf43jOvy+ny7vdh/o8QkSAggsCIhROxXqHRs0ysd7hY0rpJy9qRQUQ4fe25c/ngyccN+z6kLQjMLA7cBJwPbAWeNbOl7r4mabErgD3uPsfMLgVuAC5JV00i2SoWMwpj8YzqpsM9CIOOri66uugJjKOFR2fSd8nrvGW5MIQ6em0v+B46u7qCd3dwxwnC1IEuD2pzh67u78LpN+eDE4ZZuB/d013u4G+u0/1d9/rJy74572jLvrnNdPXTlc4zgjOAje6+GcDM7gIuBpKD4GLgu+Hne4AfmZl5pj3lJiKDZmbEDeKxzAmvbJXOm6enAVuSpreG8/pcxt07gH3A5N4bMrOrzKzezOqbmzUIiojIcMqIp2jc/RZ3r3b36vLy8qjLERHJKukMgm3AjKTp6eG8PpcxszxgPMFFYxERGSHpDIJngblmNtvMCoBLgaW9llkKfCr8/BHgYV0fEBEZWWm7WOzuHWZ2DXA/we2jP3P31WZ2PVDv7kuBnwJ3mNlGYDdBWIiIyAhK63ME7l4H1PWa9+2kz63AR9NZg4iIHF1GXCwWEZH0URCIiOS4jBuhzMyagVeHuHoZsHMYyxlNsnXftF+ZJ1v3LdP363h37/P++4wLgmNhZvX9DdWW6bJ137RfmSdb9y1b9wvUNCQikvMUBCIiOS7XguCWqAtIo2zdN+1X5snWfcvW/cqtawQiIvJWuXZGICIivSgIRERyXM4EgZktMbP1ZrbRzL4edT1DZWYzzOwRM1tjZqvN7Npw/iQze9DMNoTvE6OudSjMLG5mz5vZH8Pp2Wb25/C4/SbswDDjmNkEM7vHzNaZ2Voze0c2HDMz+9vw/8MGM/u1mRVl6jEzs5+Z2Q4za0ia1+cxssAPw31caWaLo6v82OVEECQNm1kDLAQuM7OF0VY1ZB3AV9x9IXAm8IVwX74OPOTuc4GHwulMdC2wNmn6BuBf3X0OsIdgeNNM9G/AcnefD5xMsI8ZfczMbBrwJaDa3SsJOpfsHnI2E4/ZL4Alveb1d4xqgLnh6yrgJyNUY1rkRBCQNGymu7cB3cNmZhx3b3T358LPLQR/UKYR7M8vw8V+CfxFJAUeAzObDlwI3BZOG/A+gmFMIXP3azzwboLednH3NnffSxYcM4KOK8eE44mMBRrJ0GPm7o8T9IKcrL9jdDFwuweeBiaYWcWIFJoGuRIEqQybmXHMbBZwKvBnYKq7N4ZfNQFTo6rrGPwA+BrQFU5PBvaGw5hC5h632UAz8POw2es2Mysmw4+Zu28D/gV4jSAA9gEryI5j1q2/Y5RVf1NyJQiyjpmNA/4T+Bt335/8XTi4T0bdF2xmHwB2uPuKqGtJgzxgMfATdz8VOEivZqAMPWYTCf5lPBs4DijmrU0rWSMTj1GqciUIUhk2M2OYWT5BCNzp7r8LZ2/vPjUN33dEVd8QnQ1cZGavEDTdvY+gXX1C2OwAmXvctgJb3f3P4fQ9BMGQ6cfsPOBld29293bgdwTHMRuOWbf+jlFW/U3JlSBIZdjMjBC2m/8UWOvuNyZ9lTzs56eAP4x0bcfC3b/h7tPdfRbB8XnY3T8OPEIwjClk4H4BuHsTsMXM5oWzzgXWkOHHjKBJ6EwzGxv+f9m9Xxl/zJL0d4yWApeHdw+dCexLakLKPO6eEy+gFngJ2AR8M+p6jmE/3klweroSeCF81RK0pz8EbAD+BEyKutZj2MdzgD+Gn98GPANsBH4LFEZd3xD36RSgPjxu9wITs+GYAdcB64AG4A6gMFOPGfBrgmsd7QRncVf0d4wAI7gTcROwiuDOqcj3YagvdTEhIpLjcqVpSERE+qEgEBHJcQoCEZEcpyAQEclxCgIRkRynIJCsYmZfCnv3vDPqWo6FmV1qZt80s0+b2Y96ffeomWXlIOoSDQWBZJvPA+d78DAaAElPuWaSGmB51EVIblAQSNYws38neJhpmZntM7M7zOxJ4A4zKzez/zSzZ8PX2eE6k83sgbBP/dvM7FUzKzOzWb36pf+qmX03/HyCmS03sxVm9l9mNj+c/4uwj/r/NrPNZvaRpPX/p5mtMrMXzewfw208l/T93O7p8CndU4Ce7/vZ34vM7IXwtd7MXh6m/5SSYzLxX0oifXL3q81sCfBe4Brgg8A73f0NM/sVQR/5T5jZTOB+YAHwHeAJd7/ezC4ktb7zbwGudvcNZvZ24McEfSMBVBA8/T2foBuCe8yshqBztre7+yEzm+Tuu8OwOsXdXwA+A/w83MapwIvu7kEmcImZvTPp9+eE+7s0/A3M7G7gsUH+JxMBFASS3Za6+xvh5/OAheEfVoDSsAfXdwN/CeDu95nZnqNtMFznLOC3SdsqTFrkXnfvAtaYWXeXxecBP3f3Q+HvdPd5fxvwGTP7MnAJwbgZEPTguSxpm79x92uSani0V01fA95w95uOVrtIfxQEks0OJn2OAWe6e2vyAkl/zHvr4Mim06Kk7ex191P6We9w8uYHqO8/Cc5IHgZWuPuucP77gQ8PsG7wA2bnAR8lCDSRIdE1AskVDwBf7J4ws1PCj48DfxXOqyHoDA5gOzAlvIZQCHwAwIOxH142s4+G65iZnTzAbz9I8C//seE6k8JttRI0Uf2EsFnIgtHM8pJCoV9mdjxBx2cfTTrzERk0BYHkii8B1RYMNL4GuDqcfx3wbjNbTdBE9BqAB/3rX0/Qi+aDBD1sdvs4cIWZvQisZoBhT919OUFbfr2ZvQB8NenrOwlGZHsgnD6foJfLVHyaoHfMe8MLxnUpridyBPU+KpIkHBin2t13jtDvfRUY7+5/F07fBtzmwTi4IiNC1whEImJmvwdO4M07jnD3v46uIslVOiMQEclxukYgIpLjFAQiIjlOQSAikuMUBCIiOU5BICKS4/4/fa0RlZzhWPsAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.FFT(p1,16).plot()   #Perform a 16-point Fourier transform and plot the magnitude spectrum by default"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "x[n] is sampled from the 8Hz sine wave x(t), but the 8Hz peak is not reflected in the amplitude spectrum. Because the spectral resolution at this point is $256/16=16Hz$, which is larger than the signal frequency of 8Hz, the fence effect and spectral leakage occur. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "periodicExtension(p1,16).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also in the time domain we can see that the $\\tilde x[n]$ obtained by period extension at 16 points is no longer at a period of 0.125s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.FFT(p1,32).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When using the 32-point Fourier transform, the spectral resolution at this point is $256/32=8Hz$, which is exactly equal to the signal frequency of 8Hz. therefore we can see that the 8Hz peak is reflected and no fence effect or spectral leakage is observed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "periodicExtension(p1,32).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the time domain we can see that $\\tilde x[n]$ still has a period of 0.125s.\n",
    "\n",
    "Observe the correspondence between the true frequency $f$, the true frequency $\\omega_s$ expressed in angular frequency, the normalized frequency $\\omega$, and the frequency points using different frequency axis scales."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.FFT(p1,32).plot(xlabel=\"frequency/(rad/s)\") #Frequency expressed using angular frequency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.FFT(p1,32).plot(xlabel=\"normalized frequency/(rad/s)\")  #The normalized angular frequency, 0~sampling rate/2 corresponds to 0~π"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.FFT(p1,32).plot(xlabel=\"freq point\")    #Frequency points. 32-point Fourier transform with 16 frequency points between [0,sampling rate/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then see the case where there are two frequency components in the signal (8Hz and 32Hz)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p2 = p1 + ak.create_Single_Freq_Audio(0.1,32,256,1)\n",
    "p2.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.FFT(p2,16).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When using the 16-point FFT, the spectral resolution is $256/16=16Hz$, which is less than the signal frequency of 32Hz and divisible by 32Hz, but greater than the signal frequency of 8Hz. Therefore, spectral leakage and fence effects do not occur at 32Hz, but do at 8Hz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.FFT(p2,32).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When using 32-point FFT, the spectral resolution is $256/32=8Hz$, which is less than the signal frequency and the signal frequency is an integer multiple of the spectral resolution, so the peaks at 8Hz and 32Hz can be distinguished without fence effect and spectral leakage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.FFT(p2,64).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The spectrum resolution is $256/64=4Hz$ when using 64-point FFT, and the spectrum is further refined."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.FFT(p2).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, the FFT is performed using the full 256 points with a spectral resolution of $256/256=1Hz$, without spectral leakage and fence effects. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.FFT(p2,512).plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "periodicExtension(p2,512).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The use of 512-point FFT is equivalent to extending 256 samples with 256 zeros before performing the period extension, so new frequency components appear, thus generating spectral leakage and fence effects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p3 = p2[0:48]\n",
    "aly.FFT(p3).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first 48 sample points are taken to truncate the signal, at which point the FFT is performed using the full 48 points, with a spectral resolution of $256/48=5.3Hz$. $5.3Hz$ is divisible by 32Hz, but not by 8Hz. Therefore, there is no spectral leakage and no fence effect at 32Hz, but there is at 8Hz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p2.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3rikMqOmuluskBP7uy47zuYcuUWuaCWXfWEx29N0K9hPtAn/zbVfylSdXjUcG+Fsg8RUjWwEyACulGlfOT/HGW47zPx++TNXQlO4fWqTJT3gW1nKxxmIhy5tvu5KvPrXKC4adhYvVJjPTHhZIJjWwr/1oPstbbruSB85t8sxK2XgdXoIsn03RbCvqEdyU48Rquc5iwbkeLxRr3PO0mfuoWG2SzyRJJXceD7kBNd2VUp0j+Sx3vOIkW9Umf/mYmdWuD8yCR+sOmNziW+3S+6m/cw2ttuKzD5pZy/7JHm7bHRsDGX8arTYblQZH81lec+MVlGpNHr9cMnqtVx8bOBi+9sVChtfcuIRScN/zG0av29pu+FggSeqtNvVmVFdJnaOFDK+5yWlZ883n1s3W4VGcBfH05dpPVks1juYzvOamK4AI12Pb53oMqOmulmosFjJ8z/WLpJMSaV8K2RTJxM6kk07W0YTeM6ulGnPTaW45OcuJuSm++dyG0et8kwpsFtbksO4GJo8WMizOOK3YTVuPe1WRwmSn8bbbirVynaP5LIsF3ZreLLOkv2W4ZtCOvCslxxLS6zBt+d0/jXCv6xgXtEAtZFNMpRPGCQ5+rtbuwR1NoK6WnXWkkwnmpjN7XkecB+Z+sOJeDxFhsZCNcH40EenGPDRx9tOzAiQiOgC2WMiwkHOEgckHoNlqU663dgUmwTHJa812pBTHcWFzu0GrrThayLCQjzbLY6uvZbhG3yBRDoh6s81WtcnRfIbZqTQJMZ/lUdze3SIbDsBBVapx1BWmC7lMBIHqfT1yOvYQ2YXluBaddaRZLxuuY9vf5QuTaxmuFGssutdjPpc235ftBjPZFIk+i0z307MurAlAB8COFrLMu0N2THK5tXbg7RrQN+bk3RC91yOfSZJOChuGue3hFoj59VjrWIZZEglhbjptbAn5BfMn2QJptRVrlTqLrlCfz5kPHQq3QKK6sOqdQWELuQwb2/tkgUzgvkDXIgPnemxGssi8Y4ZgLZCJQAfAjuYzzLlamolG5VdFCt0bYhKLCTsWWd4xyU1dFPWm0yjPL40Xomm6OpNF35jzuUwk1+JB03TXK3WUomOBzE+nI7iOfNKrB9B0q40WpVqz41acy5kLdq/hSdBroU7evoAbm+p8TiNYINWm5/VIJoTpdNKm8U4C3YMqSzqZYCabMtKoNn36+sBka1QdgVrouihMDgi/IjEYTNPVRXOLPTemiWVYa7aoNdsHTtPt7our6ebTxpahX0xoEF+73pejea1xR7AMfZJOOgrGBO5Ls9Vm3U3CAUfR2ao2jFKsvYZ8aeIqRrYCJCKr5TrppHQsifm86YEZYIFMsKbbdWF1TXITzd+v+ht6Z6SYXw9drNb1te99HZOs6fZfD8eFFX49lFK+yR6DpPGu9ihcYL4v4O/iTCedos9JjE2tVXYqOgu5NEp1iwSD8Es3Bz16wFogY8+qGxDU/azmp81uiC2fluEw2ZruSqmOiHMwgLmLIuh6DGSB9Gnc89Nmwdpuda+XBTK5mu5Kv0XmxoTCiiKrjTaNlvK8Hp1hX5EE+859mculqTXboZ2blVK+SRbgFptO4L70W+zzERJx/JIKYPD2P3vFCpCIrPQEBMH5AESxQDxdJROs6a6UahzJZTq5+uYuLP/rMYimu1KqkUklOsJnPpcxcmF11pE9WFlYXpp/s61C3U9Fn4Z9mlxETVe7fBd7LEMg1O273WjRaiv/dWRGO3Rsv+iNoQKdRBwT96KfRQajn9WisQIkIqs9qZFg7hrwG5sKk63p9gYEwTx4HXQ9ur528xtipVTvBPKddaQp1ZqhxYhBllA2lSA5ocO+VktO+5B5933NuZpumHD3mprZS9QhW6vl3ZYhhCeedMc/e69jUmunerMWoXs9ws6QdltRrHkH0WHwDtZ7xQqQiOiDSrNgmEXh15YB4i0E2iurpXrHzw7OwW3iogiyQKbSCRISNYi+U7DrGp0wTTdoHSLiDi+aQE23XONIPtupGdCaf5hw7zRS3CfX0WqpxlQ60YlrdTTukHWEWUJxHZh7pbeODHr2JUSgOl2QvT+nEF8/vVgFiIi8UUTOisgTIvIuj9+/WkS+KSJNEXlb3+/uFJHH3a87R7FepZR7UO3UuE2yKIrVBrlMknRy9yXPTXAab29OO5i7KII0f+fgjnZArO5yLbo1OiHC3W+crWZS28yslOqdQwp6BGro9QjW/HMR58RrBUNbhgt5LdjDLCH/pBNwXFgTKdhLNVIJ6QjoBUMXltc47F7yMbn0YhMgIpIEfgt4E/BS4MdE5KV9T3sO+CngD/peewR4D/Aq4HbgPSKyMOw1V+otqo32ThfWtFkWRVAKXi6tu5xO3g2h24dojF0U2iLL+mtUUTXdfksIwtuZ+A1P2rGOSRTsu1yLZsFavzGymqiuo5XyTkE2P21qCYWvYxIF+2qpzpF8pmMZzkyljLomhF2PuBSdOC2Q24EnlFJPKaXqwEeBO3qfoJR6Rin1ANDvyP4B4AtKqTWl1DrwBeCNw15wfwAMuhpV2A3hV0UKkEi4c9En7IaoNVsU3fYhmiguCq9GeZpc1nwWh1Jq10Fl6rIpVhuIOONavZhcF1a/a1Hvi5mm66vsRNR0d8cMI1pCvutITWQH635Xq+6aYHJ+QICikxls2NdeiVOAnASe7/n5nPvYvr5WRN4hImdE5Mzy8vJAC9Xo0a2LBY8b08AE9dt8mExNt7d9iMbURRF2PaJomDpY7qVxh7mwtqpNCpnd/YU0k+rC2uXSmzY9uMM13UhB9FJ9h4IxlU4ynU7uOQZSyCYnMmbY71oEt72L8b74W8qDDPvaKwc+iK6U+qBS6rRS6vTS0tKe/q/+nHYwz6LwK87STKKm6309zDX/IAESRdPtWoa7BbuZZRi0jtTEpVf3tw8BSLldE0yuh9PxNen5+3wmZRyr68YMszseN2nfEWoJZc3XMU6slms7BCqY1U4FFbxCbz+90V6TOAXIeeCqnp9PuY8N+7UD059bDz1BsLAPQK3JjI+/HyZT0+3k+Hto/mHXo1Rr+sY/IJqvvb8aHjBu7FiqNTwz47rrSE7cvvS3D9HM58Pbu+h90UHvfpzPqelEwSaNltqlcZs0dixVmySk25Wgn0I2RaOljKcbjguOZbhToJo0mDRxYcHoSwHiFCD3AjeIyLUikgHeDtxl+NrPA28QkQU3eP4G97Gh4nVjdn3te3RhRcw6Gge8NH9zF4V/TAi0j9vsenRTI7vrEBGjGp3QdUygprtS3K3ogFkbEb859Zp8xnzYV3+Dy+46whs76hiZnyCLs4X5oFTqTSr11q7rMW/Q4j5UgMQ05jc2AaKUagI/j3PwPwJ8XCn1sIi8V0TeAiAirxSRc8APA78tIg+7r10DfhVHCN0LvNd9bKislGrkM0mm0l2tyDSLohQaA5lAF5ar+R/xuiEMNMywmJBpVpoWZEf6NW6DdialWngsZtJ87To21X89nGDt3vcFzFLOu+vwcmGFCJBasGCPcw74oHgl4YDj9g09P2qNTtddL+LqmuD/SRkBSqm7gbv7Hnt3z/f34rinvF77YeDDQ11gHyWPdsomsycarTbbjRYFj3YZmnw2xbOrlX1b6ygouf7y/gwmExeFX8dXTRTXUanmXcth6hq4+kjO9/f5TIpqwxn21T8jfFwputdtrq+WYyGX4fm14M9YsRruWgTn4NZxJj9KPplUJm1mTJIsYLLazGhh12/hLeTSlOst6s02mZT3Z0zvS5BrsfdvjIrJuCPGhEq95emTDWvfUQoxP2EyXVjleotcOrkrg8lk9kRYUkEuk+r0Qwpdh2up9GtnZsHJkOQG1zVQaUyOdajTwXO7BLtB8LoWktygr4dBYoH+POf7BJJJY0eTJAuYrA7W2mrL9V8Pg64JJi5wGL1LzwqQCJTrzV03JYQ3VNRaQVCwNkpwclyo1JtMe1yPhXywi6LebFNrto00XRNXSaXeZCqd2FVTsmDiKjF02UxSIF1njfUrOyZdE0rVJoV9ch1VfAS7buxYDPg/TJIsYML2pea/LxCceBJmGcbVT88KkAhUat4WSJirJKxBHbgxkBgKgfZCudbqfHB7CXNRdMf77pem2+poYL2E5ddrQRaUHTeRmq6PBWIye2I/NV1fC8SgRsckyQImq/1PxwLJ7BaoECZAwpIb4nHpWQESgUqjuetmgPBgbSkkhxucm0wpp431pOC49LyvR5CLwuR6RGkwuV1vdQROL2GzJ0wE2SRqupVGi3RSdvnTTdqZFEOSCrTCYGSBBFhCYesIC+YP0rE5bvT16Fd2TPYlLNkjLkvZCpAI+FkgYeminU68QSboJGq69aZnwVmYi0JbZEHXIxdF0601fS0Q8L8xdXVvkMsmF5NmtxcqNT9Xa3DKea3pBHID65UiaP6VepNkQsj2CbIFgz5lxWoz0OXbtVAnZ186rsVsv0ANL0YOux6ZVIJ0UkZe9GoFSAScGIjXgdnNovDCRNOdVF/7tKdADXZRdLNR9k/T9VpHWAfasNx66LVAJkewl32SPbRA3fRxt5paymD2OS3XnCSL/syhsH5ptWaLeqsd6LKZxBEI/q7FcBdWmAUC8RQjWwESAccC8Q6ig38WRVfTDde4J0nT3a57a/5hLoqg2SiaKJpu2Wcdc9PBB1V3GuHB0nS3/bIFQzolG1nKnZYZ4QK1Um96uhbDuhWYrCObcmbGTFYhoXdSQc7tmuBnkek59UFlAKDH2loLZCxRSlFp+AeNwV/jDhvSAxOq6da8Yw/hmn9wozyIlu3jd2CGNXY0WcckarrlunesLmz2hIlFNp1OGg/7qvgkN4Q1djRZh4jENkRpUCr1JtPp5K5sQd01wc8yrDWdOfXhFsjo2+5YAWJIrdmm1VaeFkhYO5NSrUk6udsX3MskjrWtDGiBRAtem2X7BB2Ye1nHJLoW/WJ1YV0TirVwgaqHfZm6Fr0UjFQywcyUf2NHE1caTN5MkHLdWwEFN+U8xDIMcvlCPB29rQAxpJtB4W+SBwVrg6pIIb5WBHvBz9e+Hy6KKK6jSs07BjJnqOkGuhbTk5fc4FevFDZ7wkTzB3cqoWFyQy7t/X/NB/TDKhokWYDbsXmCOiVXak3Pzyk47UzCkz1CBEjGxkDGlrJPAAwMgsYhOe0weZpu022o55fGC8EHdyaZ2NFTrB9t2ZhoumWfbLCwxo4mFoge9jUp+wL+Lj0Iro0x6ZgAbp8yoywsbwuksw4/V5rBvsDk9Snzc+mBc4b41U51PqdhMZAY+ulZAWKIrs/wDgqGB43DtKlJS+PVrT28TPKw2RPFanALdYBkQphKJ0I1zFZbUW14CzIIbt+xVW2QSSbIpvwFGUzeTBC/pAIIbu9iqvnnMymj6Zl+Lk4IbuxobAlF6Ng8Dvi1QoLgBpMmljLE0w7JChBDtAbqdUPkQ7Iowqp7oScLK4JGVW20+MqTK8bP308qnbYMPgd3PshFEX49wEzD3A4QZBBco2O+jmgWiFKKv3xsmbZBH69hUPFJboDglu7GB5Whpht0YC4E7kt4LMZZh3nHZs09T6/FZk36xepA74t38W3YNEKNTeMdY/yqaiE8iyKsuhecQqBMMhFJ0/1PX3qSH/8vX+fyVtX4NftF2actgybIRRHW50iTM9B09e+9enI56/DXuEshxVk71hFBs/vTBy7yjz58D199atX4NfuFUsq3XgmC+7aVak0yqXCLzFTTLdf81xG2L2BgCWWTkfblkYtb/Mhvf5VPnHk+/MlDoFJr+bZjn89lqDfbniNpu+nmwQI1l03aQsJxJSgGAsHtTMI6vmqipOE1W20+fq9zI1zaHL0A2Q4QqBDmogjutKox0TDLAckNEOYaMFtHVF/7/7jnOQAuxrAvtWabtgr6nPpr/lvVZmimD5hruk4MxM+V5t/YsVhrkk0lfFubR12H5qN6X2JQuMC/FRIEJ+KYuvQKmRT1ZptGa3Rz0a0AMSQoBgLBrgGTKlLQvnazG+LLjy1zyb0R9OS3UdJx6QWY5MGuIwOBmgnXMLsN6vxuzICgca0ZqtWBm3VkqNk9u1rmK086lkcc+xKULQjBXRNKIUOcNHkDTbfebNNsq8B1KIVn4DjK58M0ZlhttPjjbzlTr1eKwR2ah4VfejX0tnfZvTaTbt7QbRM/yuLKWAWIiLxRRM6KyBMi8i6P32dF5GPu778uIte4j18jItsicp/79Z+HvVb9QY2aReFUkZq5bKLktX/03ueZSjvbF+dBNYiLolgNng+vMdEwOwdmQH79xrafb9nMhRWlYO1j9z5PQiCdlM5o2VHSsZT9NN28Lib00nQbRp9Tk3TRMMG+ENDOJIqFajoz5rMPXWSr6rT9j+N+geAYSFAxcrHaYCqdIB0y0Kyg2/+MMJAemwARkSTwW8CbgJcCPyYiL+172k8D60qp64HfAH6953dPKqVe7n797LDX2x0GE81Voj/gppqdiab7wlaVP3/0Bd7+yquB7kzwUVIOOSACXRQRXEdhmm7XteifX9/yaexoHETPpIy0ukarzSe+cY7X3HgFx+emWC2Pfl/CBHtQirXp9chnU1TqrcAkAb+ZJJq5gIaKUZIswKxW6H/c8zwvOprjb734aGcU8yjR2YL+MZCw62FyfmgL5BAIEOB24Aml1FNKqTrwUeCOvufcAXzE/f6TwGslqBpviHSGwfh8APzy60uGmS1grul++r4LtNqKO//ONRSyqbG1QLxmTyilnCC6kUsvPCbUXUewb9lPszOxhHKGsam/fmKF5WKNt99+NUfz2Zj2xT9bEIIb95UMLWWTKY2VEEsoqLFjlCQLCE99P7de4Z6n1/jRV17FUiEbiwsrLFuw22bGwyKrGVrsEWqn9os4BchJoDcd4pz7mOdzlFJNYBM46v7uWhH5loh8WUS+1++PiMg7ROSMiJxZXl4eeLGVhpOh4jcXez6X8Zw9sWXYhgDMK0mfXStzJJ/h2sU8i4VMLBZIxSAGArt9upV6i7YKT9HU/3fYzeA3YyFsHVqQmayj4LaICBv29Zw70/47r55nsZBlOQYXVqgFEhisNU32CE85N4nFgHdjR3MXllnH5u6+LLA4k2W1XBv54Da/TryaoK4JUSxDGG0t2aQG0S8CVyulXgG8E/gDEZn1eqJS6oNKqdNKqdNLS0sD/8FKreV7M4D/jWlS7azJGebXr5XrnRtwsZCNx9c+oIsiyvXQLr2gm93Etei1jq4gM9N02wrPFMteVst1RBxlYmkmHsEeltwQNHvCJN0ceqbfBRzcYS7O+Wn/4luTzg296whzYWlX4pF8hsVClkZLBU7MHAblkFid7pqw7uH2LBkK9s70zMMQAwHOA1f1/HzKfczzOSKSAuaAVaVUTSm1CqCU+gbwJPCSYS7Wr7+Qxq8Dbbe611zTDWO1VOdoPgu4AiQmV4nXsCCNn4vCtNoZnEOw1VbUfOasgElyg3ew1rRozlmrmaa7Vq4xP50mmRAWC1nWyjWjAO9+Eu5a9HZhtdvKOFvQRNPVMSO/A1M3dvTLwjL9fIDJvvQKEOf9j/qeCSsDgG7CRz9RknB6/9YoiFOA3AvcICLXikgGeDtwV99z7gLudL9/G/DnSiklIktuEB4ReTFwA/DUMBcblIIH/rMnTPsLgS6cC7dA1it1jrjZNEcLmdiCtV7DgjR+sye6nUXNNcxgV0kTEToZabvW4SPYSwadZzWm87fXy43uvuQztFXwlLlhEBYT8ps9UWm0UIYWWd5A0w0rNPVr7NhuK0p103oUNxYTcs+sactwOs1iwVG8Rm0ddsoAgs4Qn9R34zKACLNa9gsjASIiLxGRL4rIQ+7Pt4rIL+/lD7sxjZ8HPg88AnxcKfWwiLxXRN7iPu1DwFEReQLHVaVTfV8NPCAi9+EE139WKbW2l/WEUWn4F0VBd/ZE/41p0nlWU8gmqbtNCoNYK9dZcA+qxUKW9Uqd5giLhyC4XQb4xx6iaP5Gmq6pIOtbx1anunf/NN3Vcq0jQBZn4jmowlx6umvCbovM3FI2iYFshwgy6Lbv6MWJNUX8fIQI9rVynbnpNKlkokeAjKcF4peFZWYpj94CCV+Vw38B/jXw2wBKqQdE5A+AX9vLH1dK3Q3c3ffYu3u+rwI/7PG6PwT+cC9/OyqVmnfHV41fFoWe/22icfdquplUxvM57bZivdLgaM9BpZRzk1wxOxX+RvaJoIZ94O+iMK2qBTNN15l65/9/6dkTu12L0WIxzt8K13SvXcwD7DiobmQm9G/sF2HZguBdozPI9QjSdMshyQ3g1k75riOKhRq+Lx3Brl1YI44bhtUrgXOGPHppa8djrbZ5ssd0OonIeKbx5pRS9/Q9NjltMPcBZ/aF/83gl0VhWkUKZtPvdG2FviGW3BtiecQaVVCrbvB3UURxHZlouuWQ5Abwnj1hOrSodx3hvvYGR3piUzB6TbdSd9qA+GULgvfsiWgCxMC12OlRFpR4snsdUZMswtYBjgDRCtdCLkNCRm8ZBjVj1Xh1StbKk4lLrzvsa8xcWMCKiFwHKAAReRtOJtShoVJvBmoPflkUxarTUK5/jKUXnUKgAM1OxzuOFnQMxDmoVmNwlfgNC9J4uSiiuPS6LoogF1bTt5Fi8DrMhvRAT8FawI3pWIbdg6obrB19DCTIzw7eDRVNO76CoWCvt0gnJbCfVdA6ItWBGLiwtMKVSAhH8tmRFxPqGEiQQPXqmhDlfoHoDSb3iqkA+Wc47qubROQ88C+AnxvWosaRckgQHbyzKEqGOdzQ9VsHabo6o0S7zOLTdIMtEAh2UUQpWAurNwi3QHZ3Bo6UXp0JX4e2DHVsam467bQzGbWvPSRbEHSnZD/N38DVajClcdt0Hb6WUPg6kglhOh1e5LnaI0DAEe7LIy4mDMsWBOd69HdNiGIp6/9/lIWERiebUuop4HUikgcSSqnicJc1fpjcEF5ZFMWaWX8hMAuCaUtjl083hqDgVQu5wOfM5zK7Ws0Xq04sycgiM6isLddbHfeh7zqm0zy7Wt7xmA6iB93QGhPXYscydPdFRJxq9FH72mv+c7c1esiWUqqTfBBFsKeSCabSiZAsLAPBPt1t7KgtlSiuNAjv2Kwtw14BsjQz+tT3sGxB6HGDlxudmGkUSxlGPxMkcFUi8k6fxwFQSv2HIaxp7Gi3FZVG+A3hF5w01R66mq7/DaF9xtqFVcimyKYSY+sqOXtpp65hWu0MZr19KrUmV84FJw9474sj2E0EmUka73p5p2AHWJzJjKUF0jt7QrtUoriwILxrQlhyA+xs7HjFzJS7jqgCJNhlU6w23ZhhtvPYYiHL0ytl39cMAydWl/LNFoSdiThX4yhnUa9HLjPamSBhLqwZ9+s0jsvqpPv1s8B3Dndp40O16eTIh90QXi3dTdsQgJkF0u/CEpFYiglNBIiXi8I0px3Msn0q9VagXxmcA7O/sWMU16Ie9hWk6a56CJCj+ezIa3SC5qFrvFqHl6qOhmxikUG4pmvq8oWdiSdRkiwgXJDpWMeRfPf/O5rPjDxmuN1ohn5OvUoBtDvLJIgO0Tp67weBAkQp9W+VUv8Wp0r8O5VS/1Ip9S+B7wKuHsUCx4FOamTIB8Ari2KlVNtxqARhoumulurkM0mmetI04+iHZaRhTu+ePbFSqnXiBGFkkglSCQltmRF26M17zJ5YKdU6QtiEXIimu+ZlgcTQZiYsWxC82+4sl+pOhpKBRQbhmm4lYCpiZx26nUmPkF0p1cmkEqHWviZsvG53X3oskJks243WSA9ak2xBr2Jk/fkx/azm3E7Jo8I0iH4M6D2h6u5jhwKToijYnUXRaisubVY5OT9t9He6vvagG6LGkcLOD9OoDypn6pn/sCCN1+yJ8+vbnDK8HiISqumaBPO9Zk+c39jm5ILZOiA8OOkpQNx+WKNs3BeWLQjesyfOb2wbf04hXNN1khvMBFlvgsP5dWcdpk238yHtf/pjUxBP4knFKKlgt0V2fmObqXTCWAktZJNj2Y3394B7RORXRORXgK/TbbN+4NEf0PCg4M4siheKVZptZXxQTaUTJCTYAlmrNDiS8xAgI74ZIFyg9s+eaLbaXNqqRjy4/TXdhlu1H3ZQ9Td2VEp1DirjdWSTgWm8a+U6uT7LcKmQpd5qdwL2o8BxHZlaIN2D6kJEAZILmdUSNM62fx27BHuUfQlxYWnrZqEvCwtGK0DKBskNcx5dE/S+mApUpx3SmAkQpdT7gH8MrLtf/1gp9e+GubBxotsewvCGcPs/XdjYBuDKKBp3qKa72yV2tJBhrVwPHPCzn4Q17NN02pm4N/HlYo22Mr8eEOxrj7oOfVBtVZuU662IAiRY013rSxWFbqLD6ggPqm0D11F/mxmlFBc2tiPtSyFkRkq51gysht+5jp2C7Mp5844KYS6sYAtkdG7fSqMVWq/k1TUh6r7kXcE+qrPAtBfW1cAK8Mfu16r72KHANAbS387k/IaTwhr1oArUdEv1Hf5ccG6IZnt0LaojC9TtwQQqdG+IwHVEdA0Mso4wl81qT7WzZtQHlWm2oNZ09edlc7tBpd6KdnCHaLomrsVcJkkmmejsS63Z4oVibYDPR7Bg77cMY3FhhbRC0vQnnpzfMHeBQ7dz9HbAsK/9xLQX1mdwq9CBaeBa4Cxw8zAWNW6Yarr9roHz69EPqlw2GTjTeK1S72i2mm7jPvMA9V7oFkWZXQ99Q+jrEdV1FGaBhPr8+2ZPdNYRwZWWyyR5Ycv/wFkv1zuuEc2oDyrTbMH+rgnn3OtxKoprMWDYl1LKicWECHYRcRNPnHVc2hxA4XJdWL01Lb2sB1iGo5xMWDFIboBujQ5AtdFipVSL5lrs6WDtNxNmPzF1Yb1MKXWr+3UDzjjarw53aeND2JhQTf/siQsb28xNp40LCSFY063Um1Qb7V0ZGVrzXRtRymjYsCBNv4vifEfzj6bp+l6Pmllyg27s2LFANgdYR8h0xN4OyZqR74uhYIednV8Hswyd2JRXgkCt2aat/DsC716HttgHUTCCh331V6EDpJMJZqdSnsOshkXZILkB2NEp+aIrUKNayjC6sbYDzQNRSn0TeNU+r2Vs6UzfC/kA6A+qdllE9V+Co+n6ubB07nq/q8S0rfV+sW1okeUySTKpRCcGcGFjm4Vc2kgT0wS5KMJmTmgSCWEhl+nUBJzf2CaTTLDY5woMXEcmFZxeXa7578uIbma9L2G+dnCCyvp6DCJAchn/YV+d1uUhMRBwlIzVzv0S/cDs1gp5X2Ov2BQ4B+0os5VM6pUAjuTSO84PiLovZp2j9wujO7mvIj2BU0R4YSgrGkM6878NfO1H8hkevei0ZD6/sc2pkHYf/RSyqc6N1I9XqqizrvAK9v0kbDynRkS4fqnAo241etTUWf03/N5XxVCAAFx3RYFHLrrrWHcCtaY1D846UoHrqDbau2JT07pn1IhuZtNsQYDrryjw9aecETrnN7bJphK7BGAQvUWvU32CouPyNbC8r7+iwF33XaDdVh3X4omIFqpeh3YZ9rJWrnPDscKux516idEIENNsQXCux6fuu8DmdqNzPaK4FsfVApnp+crixETuGNaixg19Q0yHaFQiwq2n5njg3CagUxKjzejIBWi6a5XdKYmwN013vVznd/7qqUhZG1qgmlgSt13lXI9Ops9cRAES5MLqCDKDdZya49sXt6g32wNZhvmM/7CvrmDfWT2dSIiThjzAvjRabf7zl5+M9FrT5AaAW0/Nc2mrygtbVS64gVrTVFEI1nQ7+2Ly+Tg1T7HW5OnVMhc2tlmayZJNmRURQm/DTW8hvVau70p7d143eNvz//a1ZzvuNhNMY6jg7AvAQ+c3Ob+xjQgcizDnR+/9qISjqQD5tq5KV0q9Tyn134E3D3Nh40Sl3mQ6nTTSWG89Nc/jLxS5vFWlWG1GP6gCPthrfi6sTlvr6DfEnz5wgV/7zCPcf27D+DUmw4I0t56aZ3O7wbOrFVfzj349as2258TFimF2nF5HvdnmsctFLmxUB1oHeN+YXtXOmkE13TPPrPP+zz7KZx40n5oQJQZy26k5AO4/5xxUUa9HkKbbcS0a+PxvvcpZxwPnNriwOdjno/dv9rJdb7HdaO0qvAXnGg1SL7FSqvHLn3qIj3zlGePXdGKoRoJd78sGFza2uWImG9gSv59Cp6P3aKxe05X9G8PHIiEibxSRsyLyhIi8y+P3WRH5mPv7r4vINT2/+zfu42dF5Af2upYgyvXwIiDNbafmaCv4n9++DETL9AH3gx3gzwV23RA5g7bnfpxzNSltNZmwXQ8fFqTRN8RfPbFCud6KZI5DT4NJD+FoGswHR9MF+Maz61wuRkuNhOC+XF59sDSFATXd85192TB+TcdSNtiXm6+cIyHO/x+1eA+CNd2OYDeIgVy/VGA6neT+5zcjdSnorCPjb33rGI+Xay4sKcIP7Va6//kN49dEsUDmcxledDTHA89vDrYvuh3SiFxYYd143wT8XeCkiPxmz69m2eNEQhFJAr8FvB44B9wrIncppb7d87SfBtaVUteLyNuBXwd+VEReCrwdJ434SuDPROQlSqmhiN1KLbwNgeZl7oH5WVdzHESjqriFQP0Wz2q5Tjopu+Z4p5MJMqng9tp+6HhLVAskbFiQ5iXHZsimEgNfj15fe3/b9ig35lVHppnPpfn8w5dQKlqmDwS7Cf0sQ722QW7mCwMIdtNsQXCEzEuOzXDvM2ssR6y9gGBNtxxB404lE9x85Sz3u4Lstd9xRcR1+I+1DbIMHUUt+nGh9+Wh85u02sqom7NptqDmZSfn+Oaz62RSCW45ORdpfabTM/eLsBPgAnAGqALf6Pm6C9ir1n878IRS6imlVB34KLvjKnfQbZnySeC14jhq7wA+qpSqKaWeBp5w/7+hYNJ5VnPFzBQn5qb4+tNOgDLqQdWZfudRCLRedhreefmqB+3COdBBFUGgppMJXnrlbOd67KfrqFJvkkwIWQNBJiK87OTcntfhdY3XfWJT+nWD3Mx6Xx65uEWtaXbQmWYLam49Nce9z6wD0VKaIbjVvmmWXncd8zxwbpNasz3AvvhnYfnFppzXDXa/aMuwXG/x1HLJ6DVRkhvAsZYvbFZ5bq0SXdEZcRZWWDfe+5VSHwGuU0p9pOfrj5RS63v82yeB53t+Puc+5vkcpVQT2ASOGr4WABF5h4icEZEzy8vLAy10aSbLdVfszuTw49ZTc7TainRSWPLIDAkiyB3lldOuCevV5Ic+qJ5cLhkfdCbDgnq57dR8p5X6oK4jL013c7vBzFTwjAXfdUR2Lfprutoy9Gq5XRiwO6o+qBotxaMXzea3mWYLam7dh+vh9ZnRFe6mLdlvu2pu8M9HgAsryAIphFSw+9GbIXm/odIVJbkBum7ftoq+L6lkgmwqMbLU8UABIiIfd7/9log80P81gvXtGaXUB5VSp5VSp5eWlgb6P973Qy/jt37cfPyJzqQ4MTcdKVUUgoOTa+Xarip0zSCjLButNpe3qtx2ag6l4EHDG2LboFFeL/qGyERMFYXgA2K93DDuUtq7DoATIUOodq0jYNzwWsnfMswNmIV1fmO7E+g2jYOYZgtqdFwI9tml15lZYyZAbu1Zx35ahn5p7+C4k6oN7+SMIM5vVHjxUp58Jhl5X0yVrltOOvEpIHLWIoy2xiXM9v8F998fxMm66v/aC+eBq3p+PuU+5vkcEUkBc8Cq4WtjQ9+YUd0C0BsE83BhVRq+cwHCegJ5cWmzSlvBD9xyHDA/qMoGDft60QfElXPRai8g+IBYLdc8UzT9uO0qZx2Lhcyu2oXQdQTMalmr+FuGg9zMOuX5ldcc4Ug+E0nTNc0WBLjx+AyZpHMEHI8oUIOSG9bKdeam06SSZjk61xzNday3qIIsk0qQTorvOlIJb8vQZFiZFxc2qly1kOPmk3Pm+1IzT25w1pbietfjEVWggp5dMx4urIvuv896fe3xb98L3CAi14pIBicoflffc+4C7nS/fxvw58rpnXAX8HY3S+ta4Abgnj2uZ9/QgfST89GKCCFY010t7a521jiabtSbwXGT3HpynpPz08ZxkIrBtLleXryYZyabimyOQ3Capl+VsR/HZqc4NpuNfEjtWIePpuu3DqeuJ9q+rFcaVBttTi5Mu3VFG0avi5ItCM7h+x1XznJFxNoLgGzKf9jXmkdjySCc+ql5cplkp39aFPziGbq9jJdlGBRbC+KCWwx726k5Hrmw5VkX1E85QnKDRitdA90zA3gjBiUsC6tIt4kigLg/C6CUUrOD/mGlVFNEfh74PJAEPqyUelhE3gucUUrdBXwI+H0ReQJYwxEyuM/7OPBtnGywfzasDKxBmJtO889fewN/69ojkV/rp+k23LkSXv5ccDRd3YzOlN7eVLddNWeciVWuNzkeobgpkRD+99e/JLKWC8FV9mvlBt/1omgusV947UuYSkfv4BOksa6V69x8pfetUMgmKdf9m/150duE89ZT8/zlY8tGzfGiJDdofvbVL+ZCxM8NOId+zieTKapgB/jp77mWv33xaKRiRo1TbOodm/ITZIMU327XW6yW65ycn+bqIznqrac5e6nYURj9qERMbgD4iVddzZF8xniUbS/5EVbZB65OKTUzzD+ulLobuLvvsXf3fF8Fftjnte8D3jfM9e2Fd77+JQO9zi8Nbz0gowQG03R7e+3cemqeux+85Fg5IYH/qDEQgP/1e66N9HyN343ebivWK/VIY2kBfvxVg00hmE4nEfFxpQWMLc5lUyjltNc2Pdx7mwqmEkJbOWmjr3rx0cDXRckW1LzpZSciPb8XP/fcWrnO1UejWd+vuekKXnNTtBRejV/H5rWy/+djkPY/vU04tZv6/nMbBgKkSSohHXehCa+4eoFXXL1g/Pxe8tnUyEY7GL8jEflOEfnnIvK/icgrhrmow4zWdPuFgW5j4m+BRB9leX6j2okH3HKlcxOcvRSe8VOuhw8L2i/8+kltVRu02iqypjsoethX/4HTtQyDNd0oe3OhR4DoOoBHDfZlEAGyF/yq7IM0/6GsI+Md/1sv1z2r0GEwC6S7LzmuOjLN7FSKRy9thb6uXHMaKQ5iXQ3CoFX2g2A6UOrdOPUYR4FF4L+KyC8Pc2GHFb8Pti5WC9J0o5qtvS0sltyZImsGLa4rtfBhQfuFXz8pnWHjl5U2DLw0XV0D4usq0Xn5ETTd8xvbTKedeECUlvBOy/Dhz4DQeLXdUcqxDEcl2MG/BirQhTVA+5+ua3EKEWFxJst6OVzTN5mNsp8MWuMyCKbv6ieA21yXEiLyfuA+4NeGtK5DSyGTIpmQXQfGasiBWcimaLQUtWbLOCB6YWOb65ecbI8FjznZXiilnINqhDfEfC7TceFpgnL8h7aO6cwuARu2jkEtEH1Ipdz6kg1DwX7FzCivR3rX53RruzlSyxCcmff9zQ0brTab2/5p3vkB2v9c2Ngm0dPccCGXMZopUjaYzrifzE+nWavUI8XdBsXUhXUB6I2AZhmjtNmDRCIhHM13ZyRourn1+6Pp6lRRneUx5wqQzZAbIsqwoP1isZBhxUegRknj3fM6ZjK75ptry3DBJzbV6SwQQdN19qUbQ1jIZzpjgYOoNEYr2BcL2V3XQ/efGqUAWSpkd019XK8EW+yFgOw+P85vVDk+O0XajWUs5NI75pf7sV1vjXZfZrJUG+2RpPKaCpBN4GER+a8i8rvAQ8CGiPxmX48syz6w6HFDhBVn5SJqut052I4AyaaS5DLJUAukk1EyohgIuNej6H09/HzcQ1tHv2DvuLC8Nf9OvUQETdeZg93V1+an06H7Ao7yYFprsB8szmRYKdV3TCUMKt4b2joKGYrVJtWe9j/atRTk8oXoFkhvXcbcdMbIMizXmqPdlxGOUjYVi3/sfmm+tP9LsWgWZ7wFyHzOvzgrqkZ1rjOfvHtQmZjknWlzI/S1LxayPHh+Z43KWhwWSIBgD9N0TQW7noPdW4E8b+wqGW0MZKmQpe4mEehGl53Y1Ahdi/rA1Cm2zvfBlpBWgKJ0Sj6/sc3L3WJU2DkWOIhKvcXiSBUdPRm1xouO5of6t4w+bW4/LMuIWMxnePKFnY3a/AbjaHIR0xJ7M0o087k0m4YWyChN8qOFDKvl+o4OxWvlOtPp5Eg1u6OFDJV6i0q9W2+hXY1+BXBRB/zoOdi9BWQLuTRPr5QDX9dqK6qN9kizsI72HFT9AsTPpTecdbgad7HWESBhgj2RkEidktttxcXNbf7erd2054V8hu1Gi2qjFdjZoFxvcnU2elHxoGiBulwc/sx30yysHxSRb4nImohsiUhRRMLz1ywDoS2QftdAkFugENEkv9BTRKiZz6VDNd1uY7jRmuStttqR2z5Isdp+rAPYEZ9arzhtO9J+lmGn6WA0wd7rKjGxQLYboxfsXtdjNRYLJOP+7a51uG7gSovS/melVKPRUn0uLDduGBKf2o7YfHSvdC2y4buwTGMg/xGnpchRpdSsUmpmL1XolmAWCxlqzfYOt0fYgZkL6NXkxXKpRjIhO/7P+VwmNCgYSwxkZrdPd61cH2kKL9DprLzcs46wmgctaE013WU31tObTTWfS1OsNgMb/+n/P25f+3oMlmFnHcXdgiyo0DQfof3PCx77ov9vE7dv1A4Be6FjGY6LBYLTOv0h1asSW4ZG98bceUMEHZhdX7vZDVGsNne1Ql/IpUOzfbSFM0pfu9Ywl/sESNQq9L2vo+sq6ayjFCzY9bCvkqFgL1Z3t0LX7zNI0+2MGR6xZQi7BXtclmH/5yPIMoRo9RLFqvO8mZ7WIjqhJUjpUkqNvMAznUwwn0uPVRD9/wDuFpEvA51VKaX+w1BWdcg52nEN1Lh2MW/UtqOj6RoeVCVXgPQy72aVeE1D1ESZArhfeLlK1sp1bogwo2U/ONpxlexcR1jbDqcy2FCw13YfVPM9NTp+bWY6yQ0j1HQXcmlEdis6oxYg05kk+UxylystbB15nwp2L7Q3YLZHsM91BIi/pl9vtWm21UgVLnAKW8fJhfU+oIJTCzLT82UZAr1ZFOBoP2HFWVGzfbaqTQrZnYHO+VyatuoeYl50gugjzsKCnZruatm//9Sw6LoGejTdSnjbjqiabjq5c8rifMcC8T+o4oiBpJIJjuQysVsgsDtzcd1EgGTNXVjaMixkey0Q5/8PskCiTmfcL5zU9+G7sEw/bVcqpW4Z6kosHbq+ducDoDWJIBdWNpUgmRBzTbfa2G2BdG6I+q754xpt4YzSxz0/nSaZkM4BsV1vUW20R1oDAk6tzOxUqrMOpZTRQRVl+p2zL+kdrsV5dy+C2maUY4iBwO4anTgsw846+gTZVUdCLMNsimfXKkb/v5cLa96ge0M5LgEyk+WRC8PPczK1QO4WkTcMdSWWDkfyGcc14N6YYVXo0G2vbWqBlGpNZvqsCJN2JlpjG2UQXVfna42qk+M/4hgIaE3XWcfWdpOmQduOKLNaStXmDi0XzIK1lRhiIKCLCftiU3FYIIVMn4UanPYOug18NBdWoUeATKeTZFKJQBdWJQbXIjhK6PIIYiCmAuTngM+JyLZN4x0+qWSChVzXh2maGunXVM6LolcMpMcC8aNSbzrDhCK0pt4PFgvZzvWIo9q5dx36oDJt25GPMJXQc1/y4emineSGER9Uzr44+7Fdb7HdaMW2LzoG0rEMQyxUx7VoJti3qg0yqcSOPnMiEtrOJI7kBuhW59eaw21nYlpIOCMiR3Am/0WfCmSJTK/G3clpD7kh/Ab8eFGqNXdk+kDXJA+6ISr11sgDguC477RLL45OvJrFQqbT8j6s35Imn0lxectsaFOxtluAzGSdBptBFoiOgYzaVXI033VhrYV0Jh7qOgpZ1ip1mq025XqLZlsZxKbMh32Vqk3P4U7z08E1Op26qREL9qM9iSeDjMU1xbSQ8GeALwOfA37F/ffdQa+x7I2dmq5Z2w7T+dtKKYrVxg5zHMxcJWV37vaoWerxtZu49IZFbz+s1ZAW+5oomm7RI7lBREL7YXVci6O2QGYylOsttuutnsaSo9+XpUIGpRwhZvr5yPcM+wqj6OFaBEfpClS4avEF0WH4/bBM/RC/ALwSeFYp9RrgFTgNFgdCRI6IyBdE5HH3X8/RWyJyp/ucx0Xkzp7HvyQiZ0XkPvdrsFFmY0xvVolp2w5nKmG4AKk12zRaapemqwPnYTfEqM1x2FmdH0e/pc46Clk2txvUm21jV5rWdE0oVhvemm5Im5lKvYkIA43r3Qu9B1Un2SMmFxY4xXNr2rUY5sKK0P5HJzf0s5DLsBGQHVeOyQLpz+QcFqaftmrPLJCsUupR4MY9/N13AV9USt0AfNH9eQeuy+w9wKuA24H39Aman1BKvdz9emEPaxlLFgvdlu4mmT7gPeDHi05GSZ9GlUyEz54o10dbVavR1fnleou1cp1UQpidjmMd7uCtcj20E68mShpvqdbcZRlCeDuTcs1pGT6qqXeapR4BYurSGwa6W8Fqucaam61mkl4NZu1/SjV/CyTIMowtucGjGHkYmAqQcyIyD3wK+IKIfBp4dg9/9w6cCYe4/77V4zk/AHxBKbWmlFoHvgC8cQ9/c6JYLGQp1pwW1WFV6Jp8NmlkgXhVO2vCZk9s1+OxQPQhvVKsdTJ9Rn1Yws4GgmslM8swn0nSaCnqTf9WJKBdi7tjIBA+e2K70Ry5mwR6r0e9o/DEYRlqYbFSqnUtkNDsOPMO1n77Mp/LsFlp4Neko1t4O/rkBnAtw1KNj97z3FCmFBoJEKXUDymlNpRSvwL8n8CH8D70TTmmlLrofn8JOObxnJM4LVQ059zHNL/ruq/+Twk4SUTkHSJyRkTOLC8v72HJo6XTvqNY47HLRY7PhucumGq6XjntGkfTDc4qmU7HoPn39MN65FKRE3Px5HL0ts141HAdpprudqNFq608BbvTpyzYAolDgPQeVI9eKpLLJD0/V0Nfx0zXhfXIxSLppHTW5ke3AamZ1e7twkpTb/kPb+qm8Y52b3R1/kqxzh998zzv+qMHd01t3A8iO0yVUl9WSt2llAq0jUTkz0TkIY+vO/r+PwVE7bH1E0qplwHf6379ZMB6P6iUOq2UOr20tBTxz8SH/vD/8bfOc3GzyltefmXoa0ybw3Vy2r1M8ul0aBpvLDEQV6D+zROr3P/8Bm+5Lfx6DAPtsrnvuQ3+5skV3mywjryhpluqBu9LsKskHteitkCeWS3zmQcu8uZbr/RtgzNMZrIpMqkE5ze2+dR953nDS48HtliHbvsfMwtkd+Et9BYTet8z5XqLTDIR2JNrWCzOOLUg/+Pe5/jOq+d5ybH9bx4ytHellHqdUuoWj69PA5dF5ASA+69XDOM8cFXPz6fcx1BK6X+LwB/gxEgOFFqAfPhvnuZIPsPrX+plpO0kn011tNggAl1YYXnttVYsB5U+uH/3K0+TTgp//ztPjXwN4GQdAXzkq88A8COvvCrg2Q55Q013K8Ay7J094UU5puQGXZ3/sXufZ7vR4u23h1+PYSAiLBWyfOq+82xUGkbrMB2BoJRy0969LXbwTzyp1JsjHX3Qy2Ihy189vsxTy2XefvvVQ/kboxeLDnfhtIfH/ffTHs/5PPAGEVlwg+dvAD4vIikRWQQQkTTwgzgjdg8UWrPbqDT4+684uaOAyQ/TqYThLqyAeoN6c6SzDTQ6NXSj0uANNx+PJVALji97Op1ko9Lg1TcsdQYYBaEP9rAU65JHI0VN2OyJSiMewQ7OQbVRaXDjsZkdE/tGzdGCM47g1MI0333dYujzTV2LlXqLtvK3DCFIgIx2HnovR/PO9ShkU/xgzyCs/SQuAfJ+4PUi8jjwOvdnROS0iPwOgFJqDfhV4F73673uY1kcQfIAcB+OVfJfRv4Ohkyv/9ZUq+vMBAnRdIMFiP/siXZbOQdVDIWE6WSi02rlx145HG3KFG2F/JjhvuiDKizBIdgyDK7RqdTicS1C97P69tuviiWxoX8dP3r6KiM3mmkab/d+8U46gYB9qceT3ADduNBbXn7l0JSLWESjUmoVeK3H42eAn+n5+cPAh/ueUwa+a9hrjJuptBOMvOn4DNdfYea7NNV09Q3hVVHeO3uiv3V4tdlCqdEHBDVLM1kKUyn+znVHY/n7nXUUsmzX27z2O8LditATAzHcFy9NN2z2RCWm5AZw9iWTSvBDrzgZ/uRhrqOQJSHww6ejKVzh++J24g2IgfhlLsaV3ABdt+8wFa54PnEWIz7wttu4djFv/Py84VTCUq3BdDrpGdgLmj2hNbU4XFgA73nzzUylE7EEaXt515u+g1ZbGQdGtWAP03RLAZZh2OyJckzJDQD/9DXX8UOvONmJB8TFP3n1tXzfjUscN8zQy6QSZJKJTr8qP7xmtGjmp13XajnIAonnmP3RV17FqYVpXnZqbmh/wwqQMeaNtxyP9HxtUZhYIH6plkENFbdjymnXfPf14X7tUXD7tUciPT9vGJvaMnJh+Vsgce3LzVfOcfOVwzukTLn+CnNrXePMBDGzDL06BGRSCfKZZOC+nJjzHo0wbK6cnza2xgYlrhiIZQjkO/O3w326XuY4BLtK9AEYl6Y7qXRdWGa+dm8Xln+2T6PVpt5sx2YZTjI5g6mE3WFS3oJgPqCdSZyCfRRYAXKAMNV0ix6deDXaJPcKCnaHSR3cG2IYTKUTJCTc116qORluSQ8X3VQ64Tt7QhexjXqY1EHAZARCkGsRghsqlmvxBdFHgRUgBwhzTbexqw+WJmj2RNwxkElFRIzmb3t1SO79P/xqdCp1/6QISzC5bPgIhI5l6Gu1+3cJsBaIZWLoBmvDNSo/bSpo9kRcfX0OAiZtZrxmtPSy4FOjU4lpbOpBwGQEQrHmdDou+Hzu/SwQpVRsnRtGhRUgBwh9sO8liB40e6JiYyAD4wRrwzXdoD5Sc9M+FkjHMrSCPSomY22L1QaFTMo3+8/pyLtbsNeabdrqYCtcVoAcIJIJYTod3pG3WG34BgTBf/ZE2fraByafDXdhbfkMLdL4zZ7ozpyw+xKVnKFg93NfgbMvm9sN2n0thMoxNVIcJVaAHDDCZoK02opyvRWo6fq1M9GdRa2mGx0TTbdUbTAb4MLymz3RGZtqYyCRKRgI9iCXLziWYVt1YyWaw+BatALkgBE2EySo35Jmwfegci2QGEbaTjqmLqwgC0S3dO+fPdEZWnSAD6phkcukwtPea41QyxB2Zy52h0kdXMFuBcgBI0zT7fZbCj6oNn3SeHOZZOyV4JOIiQsrLAaykEvTaKldWUOdudsH+KAaFoVskrpbR+OH3ywQzULeu53JYXAtWgFywAjTdLsWSICrxCeIXq7H19dn0sllUoH70my12W60gvfFZ/ZE56CylmFkcgbtf8JdWD4WSO3gZy1aAXLACNN0g6qdNX6zJyq1+Pr6TDqFkJYZnSFfIZYh7K5G7/jabXZcZAoG7X+2DCxD2N3+x1oglokjzIUVVlULXU23v5iwYi2Qgcllgod9BbXY1/i1M6nUm6QSQiaGqXeTjha6QcWEpVojtD4Hdu/Lto2BWCaNMBfWlkkMxMckL9WaB/pmGCaFkJkgHQESGET3dmGVqk5sKs5ZHJNKWAPSRqtNtdEOtNhnp9OI7G50WexkLR5cpcsKkANGWMVz0HAcjV9DxbVynaMxTQKcdMLG2gYNk9L4zZ5YLdd3DCCzmBM21tbEMkwmhNmp9K7Ek7WS8/PCAb5nYhEgInJERL4gIo+7/y74PO9zIrIhIn/a9/i1IvJ1EXlCRD4mIgd3hyKiey71p3pqOr72kHRR2O3TXSnVd80IsZjRaTPjY4EYxUB8Zk+sluqdEciWaORCphKWDGKG4J36vlquMZ9LG8+NmUTiemfvAr6olLoB+KL7sxcfAH7S4/FfB35DKXU9sA789FBWOYHksynaCqoN77TEYrVBMiGBsYzeoVKadluxVq6xaA+qgQibSmii6frNnlgt1ziat4J9EMIskKAZLb3MeRTfrpYOvsUelwC5A/iI+/1HgLd6PUkp9UWg2PuYOI7e7wc+Gfb6w0iYpquL1YL85V5BwfVKnbbiwN8QwyIXMpXQpD4HvGdPrFgLZGDC0niDhkn1spBL70o6WS7VDrzFHpcAOaaUuuh+fwkwGy7tcBTYUErpHT8H+A5jFpF3iMgZETmzvLw82GoniDBNtxRS7QzesydWXbfJQb8hhkWor13X5wT0KIPdnV+brTbrFetaHJRuGq+PC8vAtQi6dqrfAjn4FvvQUmpE5M8Ar5msv9T7g1JKiYi3w34fUEp9EPggwOnTp4f2d8aFsPnbW9UGs9PBh5SePdF7Q6yUagBW0x0Qren6WYZb203SSWEqHazT9bd0X680UIoDf1ANCz3sy88C2XKtiqAeZeBahuXdyQ0H3bU4NAGilHqd3+9E5LKInFBKXRSRE8ALEf7rVWBeRFKuFXIKOL/H5R4YwqYShhVFaZwhOd0bYtXNKLHZPoNRMMjCmplKh6bizufSXNjY7vy8WnYF+wE/qIaFHvbll8Zr6lpcyGUo1po0Wm3SyQSNVpuNSuPAK1xxubDuAu50v78T+LTpC5WTXvQXwNsGef1BJ2cQrA3TpmD37IlV1wKxAmQwugVrQfsSLtj7Z090BfvBPqiGSS6b9G2oaJL2DruLb9fLh0PhikuAvB94vYg8DrzO/RkROS0iv6OfJCJ/BXwCeK2InBORH3B/9YvAO0XkCZyYyIdGuvoxJkzT3dpuGB1U/a6S1XKdhDi+Xkt08iHDvraqwdXOmv7ZE13X4sE+qIZJPpui5GuxNzoxwSDm+9qZrBwSwR5LWbFSahV4rcfjZ4Cf6fn5e31e/xRw+9AWOMGEjbV1XCUGAiSfZuO5rgWyUqpzJJ+1nXgHRA/7CrIMTfZlPpfpzJ6Yy6WtBbIPFAKKb8M68Wr6Mxc7rsUDLtgPboXLISUfEKxttxXFWjM0iA5Oh9He2ROHIaNk2OSzyc5Ux34cyzB8X7QFqK3D1XKNlFsJbRmMXMbfhbVVNbPY+2untGA/6GnvVoAcMPIB6aJOhXp4QBB2z55YLdtag70S1GbG1ALpnz2xWqpzJJ+xluEeKGSDguhRLRDtwrIWiGUCyaQSpJPiqel2i6LMb4iOpluy1c57JWgmSNEgvRq6bWbWe3ztB/2QGja5TMo/jbdqZrHP9/WPWy3XSSfFyHqZZKwAOYD4abqmbRkA5vpvCFvtvGf8ZoI0W+3QOfUa7cLa6HFhWdfi3shnU76FhMVts5hhIZsilZBdCtdB75BsBcgBJO+j6Zr0W9L0BgWrjRbFWvPApyQOGz9N12RKpGZXsPYQ9FsaNvlMMtgCMbhfRMTpErB9uBQuK0AOIHkfTbdTVWtgki/0zJ5YKx+OgOCw8fO1b22b9VuC3bMnVg9Bv6Vhk8+mqNRbndToXpwgulmCwnwu042BlA+Ha9EKkANILuM91jaKBTLXk9d+WAKCwyaXSXpOvoviWtSzJzYqdbbrLcr11qHQdIeJTn2v9I1wrjZa1Jtto/sF3H5YbjuTlWKNxUOgcFkBcgDxy2vXB5VZuqjz4V8rN7opifag2hN5PwtE78u02UG1kEuzVu4K9kWb3LAn/DIXO0knhsWz827xrVLKabF/CO4XK0AOIH5jbaNYIJlUguuvKPCVJ1fsQbVPaMHeP+wrSnYcwHecmOXrT6/xQtE2uNwPCj5jbU37YGleemKGxy4XeXa1QrXRPhQWuxUgB5C8jwtrq9ogk0owlTab0fzmW6/knmfWePjCFmAPqr2SyyZpK6g1dw77iipA3nzblSwXa9z9oDMR4TAcVMOkMxOkT+kaZF/aCn7/a88ChyNmaAXIAcQ3jXfbLKNE8+bbTqAU/OE3zjGVTgROMbSE46fp6uQGU033+2+6gnwmycfvfR44HAfVMNExkF37EiE2BXDDsRluOj7T2ZfDkLVoBcgBJOfTMqNo2LBP8+KlArecnKVYax6KnPZhE6bphg0t0kylk7zh5uOdIVTWMtwbeZ+phFFcvpo333blodoXK0AOIIVMinqzTaO101VimtPey5tvvRKwzfr2g0KAppvLJEknzW/HN992AnAyu7RgsgxGPsQyNA2iQ/d+gcPhWrQC5ACSy/pputEsEIAfvE0LkIN/Mwwbv/nbph2Se/me65eYm07bfdkHOmm8dW/LMMreXH00x21XzQOHw7VoVZcDSEfTrTc79Rzg3BAn5qYi/V8n56f5R3/7Rbz0xOy+rvEw4qfpmg756iWTSvDzr7meje16+JMtgfin8TYQcSz6KPzc913HZx68aJysMslYAXIA6frad5vkM9nobb/fe8ct+7Kuw46fprs1gAUC8E9e/eJ9WddhJ5fWM3T696VJIZuK3On4jbcc5423HN+39Y0z1oV1APHPa28aF6tZ9h+/qYRFw46vluGQSiaYSid2pb5HaWNyWIlFgIjIERH5gog87v674PO8z4nIhoj8ad/j/1VEnhaR+9yvl49k4ROCTrft1XQbrTbbjVbkGIhl/8hnAyxDuy+x4jQg7d8Xsxkth5m4LJB3AV9USt0AfNH92YsPAD/p87t/rZR6uft13xDWOLF4+doHCQha9pfOuGGPYK3dl3jxqp0qWgsklLgEyB3AR9zvPwK81etJSqkvAsURrenAUPAIChYj9MGyDIdsKkk6KTsEu1JqoCC6ZX/xmgliXb7hxCVAjimlLrrfXwKODfB/vE9EHhCR3xAR31xGEXmHiJwRkTPLy8sDLXbSyHlourpluNV04yWXSe1wYdWabeot846vluHgNRNka4C098PG0ASIiPyZiDzk8XVH7/OU01ludyP+YP4NcBPwSuAI8It+T1RKfVApdVopdXppaSnq25hIAi0QG6yNlUKfprtl92Us8HZhRS+8PWwM7eoopV7n9zsRuSwiJ5RSF0XkBPBCxP9bWy81Efld4F/tYakHjul0kkwy0RmvCb19fewNESez0+nO0CGINkzKMjzmptM8vVLu/Oy4Fq0FEkZcLqy7gDvd7+8EPh3lxa7QQZzmTG8FHtrPxU06IsKxuSyXN6udx7Yidha1DIcTc1Nc2uruS9SW4ZbhoPdFt9ov11u0ld2XMOISIO8HXi8ijwOvc39GRE6LyO/oJ4nIXwGfAF4rIudE5AfcX/13EXkQeBBYBH5tpKufAI7PTnGxV4Bs2yD6OHBsdopLVrCPHcdmp6g3251RwYP0wTqMxCJelVKrwGs9Hj8D/EzPz9/r8/rvH97qDgbH56Z58NxG5+eoHV8tw+HE3BSr5Tq1ZotsKtljgdiDKk50i59Lm1WO5DM27d0QW4l+QDk+m+XiZtckL7ptGZIR2zJY9pfjs85B9cKWM02wOzbVHlRxckwLkK1twKa9m2IFyAHl+Nw0tWabTdcUH7TfkmV/Od45qBw3VneYlD2o4qRrgTiC3SadmGEFyAFFa7o6DmKrascDLUC6+9IkIU4dgiU+lgpZEgKXNrUFoi1De88EYQXIAaVf093cthbIOKD3RWfIbbp9sOy0x3hJJRMszWR33C9gLZAwrAA5oBzvCQoCPL1S5uojuTiXZAFmsilymWTHArH7Mj70Zi4+tVwml0mymLcDu4KwAuSAcsVMFhFHgGxU6lzeqnHj8Zm4l3XoERGOz01x2dV0H71UtPsyJvTuy9lLRW44NhN5FshhwwqQA0o6mWCxkOXSZpWzl5x+lPagGg8cTXeb1VKNlVKNm+y+jAW9Fshjl4vcdMzuSxhWgBxgdHXt2cuOALnpuB1LOw44mm6tsy9WsI8Hx+emKVabPLdaYbVct/tigBUgBxhd9fzopSJz02mOzVp/7jhwfNZxlTxy0QqQceL4nHN/fOkxpzWftQzDsQLkAHNiznGVnHX97DbTZzw4MTdFs634yhMrHMlnWCpYwT4OHJ+dBuDLZ52xD1awh2MFyAHm2OwUW9Um376wZbWpMeKYW6PzlSdXufGYFezjgs5c/MqTqywWshy1gj0UK0AOMLq6drvRstrUGHFiztF07b6MF7r4drvRsgqXIVaAHGD0DQHWnztOHJvrarZ2X8aH6UySObfy3Ap2M6wAOcBokxzgJTYlcWxYzGdJufUF9qAaL7TVbvfFDCtADjBagJycn7bN+saIREI6cZAbrGAfK/S+3Gj3xQjb6OUAk8ukmJ1KWW1qDDk+N0Ui0Z1fbxkPTsxNIWItdlPsp/eA8643fQcvXsrHvQxLHz/3fddRabTiXoaljx+7/WpuODbDtO2ObITogUMj/aMiR4CPAdcAzwA/opRa73vOy4H/D5gFWsD7lFIfc393LfBR4CjwDeAnlVL1sL97+vRpdebMmX17HxaLxXIYEJFvKKVO9z8eVwzkXcAXlVI3AF90f+6nAvwjpdTNwBuB/ygi8+7vfh34DaXU9cA68NPDX7LFYrFYeolLgNwBfMT9/iPAW/ufoJR6TCn1uPv9BeAFYEmcqqvvBz4Z9HqLxWKxDJe4BMgxpdRF9/tLwLGgJ4vI7UAGeBLHbbWhlGq6vz4HnAx47TtE5IyInFleXt77yi0Wi8UCDDGILiJ/Bhz3+NUv9f6glFIi4huIEZETwO8Ddyql2lHbPiilPgh8EJwYSKQXWywWi8WXoQkQpdTr/H4nIpdF5IRS6qIrIF7wed4s8Bngl5RSX3MfXgXmRSTlWiGngPP7vHyLxWKxhBCXC+su4E73+zuBT/c/QUQywB8Dv6eU0vEOlJM29hfA24Jeb7FYLJbhEpcAeT/wehF5HHid+zMiclpEfsd9zo8ArwZ+SkTuc79e7v7uF4F3isgTODGRD4109RaLxWKJpw4kLmwdiMVisUTHrw7kUAkQEVkGnh3w5YvAyj4uZ5w4qO/toL4vOLjvzb6v8eRFSqml/gcPlQDZCyJyxksCHwQO6ns7qO8LDu57s+9rsrDdeC0Wi8UyEFaAWCwWi2UgrAAx54NxL2CIHNT3dlDfFxzc92bf1wRhYyAWi8ViGQhrgVgsFotlIKwAsVgsFstAWAHSh4i8UUTOisgTIrJrTomIZEXkY+7vvy4i18SwzMgYvK9Xi8g3RaQpIm/z+j/GFYP39k4R+baIPCAiXxSRF8WxzqgYvK+fFZEH3S4Nfy0iL41jnYMQ9t56nvcPRESJyESkwBrs2U+JyHJPd42fiWOd+4ZSyn65X0ASp2X8i3Hax98PvLTvOf8U+M/u928HPhb3uvfpfV0D3Ar8HvC2uNe8z+/tNUDO/f7nDtCezfZ8/xbgc3Gve7/em/u8GeAvga8Bp+Ne9z7t2U8B/2/ca92vL2uB7OR24Aml1FPKGZH7UZzhV730DsP6JPBaidpjfvSEvi+l1DNKqQeAdhwL3AMm7+0vlFIV98ev4XRwHndM3tdWz495YFIyYkzuM4BfxZk+Wh3l4vaA6fs6MFgBspOTwPM9P3sNq+o8Rznt5DdxGjqOMybva1KJ+t5+GvjsUFe0Pxi9LxH5ZyLyJPDvgX8+orXtldD3JiLfCVyllPrMKBe2R0w/i//Adad+UkSuGs3ShoMVIJZDg4j8Q+A08IG417JfKKV+Syl1HU6H6l+Oez37gYgkgP8A/Mu41zIE/gS4Ril1K/AFut6MicQKkJ2cB3o1Aq9hVZ3niEgKmMMZcjXOmLyvScXovYnI63CmYb5FKVUb0dr2QtQ9+yjw1mEuaB8Je28zwC3Al0TkGeBvAXdNQCA9dM+UUqs9n7/fAb5rRGsbClaA7ORe4AYRudYdaPV2nOFXvfQOw3ob8OfKjY6NMSbva1IJfW8i8grgt3GEh+f0yzHE5H3d0PPj3wMeH+H69kLge1NKbSqlFpVS1yilrsGJW71FKTXusxhM9uxEz49vAR4Z4fr2n7ij+OP2Bfxd4DGcbIpfch97L84HGGAK+ATwBHAP8OK417xP7+uVOD7bMo5F9XDca97H9/ZnwGXgPvfrrrjXvE/v6/8BHnbf018AN8e95v16b33P/RITkIVluGf/l7tn97t7dlPca97Ll21lYrFYLJaBsC4si8VisQyEFSAWi8ViGQgrQCwWi8UyEFaAWCwWi2UgrACxWCwWy0BYAWKxjBARmReRf9r32GdFZBL6c1ksO7ACxGIZLfM4HZ0BEJFp4KhS6lxsK7JYBsQKEItltLwfuM6dBfEB4H/BKZRDRN7fM7fk/45xjRaLEbaQ0GIZIe4Asj9VSt3i/vybwKdwKpO/glOZrERkXim1Edc6LRYTrAViscTLdwN/jTMWoAp8SET+PlAJfJXFMgZYAWKxxISIvBh4XilVV85smdtxhpT9IPC5WBdnsRiQinsBFssho4jTrhzgTbiCQkQKOGN37xaRvwGeiml9FosxVoBYLCNEKbUqIn8jIg8BF4F/4v5qBvi0iEwBArwzrjVaLKbYILrFEgMikgX+Rik17kOSLBZfrACxWCwWy0DYILrFYrFYBsIKEIvFYrEMhBUgFovFYhkIK0AsFovFMhBWgFgsFotlIKwAsVgsFstA/P/nKg9rP0T49wAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "periodicExtension(p3,48).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results of the periodic extension also show new frequency components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.FFT(p3,32).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sspectral leakage and fence effects are still not observed using the 32-point FFT."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "periodicExtension(p3,32).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No new frequency components appear when periodic extension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.FFT(p3,256).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the signal is truncated to 48 points, the 256-point FFT is only an FFT of the signal after zero-padding. Therefore, new frequency components are bound to appear.\n",
    "\n",
    "After all this, you should have found that the new frequency components brought about by the periodic extension from the time domain and the spectrum leakage brought about by the fence effect from the frequency domain are actually two explanations for the same phenomenon. So is there a unified way to quantify this effect? That is, what is the so-called new frequency component?\n",
    "\n",
    "Remember how we truncated the audio signal at the beginning? The truncation was done with the window function $w[n]$. $x[n]=x_d[n]w[n]$​​, so $X(e^{j\\omega})=\\frac{1}{2\\pi}\\displaystyle\\int_{2\\pi}X_d(e^{j\\theta})W(e^{j(\\omega-\\theta)})d\\theta$​​, in other words, the spectrum of $x[n]$ is the convolution of the spectrum of $x_d[n]$ with the spectrum of the window function. The spectrum of $w[n]=\\begin{cases}1\\quad 0≤n<N_{max}\\\\0\\quad others\\end{cases}$​​ is $W(e^{j\\omega})=\\frac{1-e^{-j\\omega N_{max}}}{1-e^{-j\\omega}}$​​. Assume that $x_d[n]=sin\\omega_0n$ is sampled from sine wave $x(t)=sin\\omega_0t$​​, whose spectrum is $X_d(e^{j\\omega})=\\frac{\\pi}{j}\\displaystyle\\sum_{l=-∞}^{+∞}[\\delta(\\omega-\\omega_0-2\\pi l)-\\delta(\\omega+\\omega_0-2\\pi l)]$​​, then $X(e^{j\\omega})=\\frac{\\pi}{j}\\displaystyle\\sum_{l=-∞}^{+∞}[\\frac{1-e^{-j(\\omega-\\omega_0-2\\pi l) N_{max}}}{1-e^{-j(\\omega-\\omega_0-2\\pi l)}}+\\frac{1-e^{-j(\\omega+\\omega_0-2\\pi l) N_{max}}}{1-e^{-j(\\omega+\\omega_0-2\\pi l)}}]$​​. If the sampling is $\\omega=\\frac{2\\pi k}{N}$​​, there will be $\\begin{aligned}X[k]=X(e^{j\\omega})|_{\\omega=\\frac{2\\pi k}{N}}&=\\frac{\\pi}{j}\\displaystyle\\sum_{l=-∞}^{+∞}[\\frac{1-e^{-j(\\frac{2\\pi k}{N}-\\frac{2\\pi k_0}{N}-2\\pi l) N_{max}}}{1-e^{-j(\\frac{2\\pi k}{N}-\\frac{2\\pi k_0}{N}-2\\pi l)}}+\\frac{1-e^{-j(\\frac{2\\pi k}{N}+\\frac{2\\pi k_0}{N}-2\\pi l) N_{max}}}{1-e^{-j(\\frac{2\\pi k}{N}+\\frac{2\\pi k_0}{N}-2\\pi l)}}]\\\\&=\\frac{\\pi}{j}\\displaystyle\\sum_{l=-∞}^{+∞}[\\frac{1-e^{-j(\\frac{2\\pi k}{N}-\\frac{2\\pi}{N_0}-2\\pi l) N_{max}}}{1-e^{-j(\\frac{2\\pi k}{N}-\\frac{2\\pi}{N_0}-2\\pi l)}}+\\frac{1-e^{-j(\\frac{2\\pi k}{N}+\\frac{2\\pi}{N_0}-2\\pi l) N_{max}}}{1-e^{-j(\\frac{2\\pi k}{N}+\\frac{2\\pi}{N_0}-2\\pi l)}}]\\end{aligned}$​​, where $k_0=\\frac{\\omega_0N}{2\\pi}$ is the frequency point in $X[k]$ that represents $\\omega_0$, $N_0=\\frac{2\\pi}{\\omega_0}$ is the sine wave period expressed as the number of sample points in $x[n]$. Thus, when $N_{max}$ is an integer multiple of $N$ and $N_0$, $X[k]$ only has a value at $\\pm k_0+Nl,l\\in Z$ and the rest is 0. The spectrum of the window function is then hidden and we only see the spectrum of $x_d[n]$; **otherwise, the spectrum of the window function is shown**.\n",
    "\n",
    "That is, to mask the spectrum of the window function, it is necessary to satisfy: \n",
    "1. The number of truncation points is an integer multiple of the number of discrete Fourier transform points\n",
    "2. The number of truncation points is an integer multiple of the period of all components of the signal\n",
    "\n",
    "If these conditions are not met, we observe the spectrum of the window function in the spectrum, which is the \"new\" frequency component from the period extension, and the \"new\" frequency component from the spectrum leakage. The second condition is very demanding and often cannot be satisfied in practice. Therefore, it is very, very normal to observe the spectrum of the window function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "input1 = ak.create_Single_Freq_Audio(0.02,8,256,1)\n",
    "aly.FFT(input1,256).plot(0, 256)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For an audio with a sampling rate of $256Hz$, the number of points of the Fourier transform $N=256$ is taken to calculate the amplitude spectrum, then each frequency point represents a real frequency of $1Hz$. The frequency points $k=0$ to $k=255$ of the amplitude spectrum cover all the power information from $0Hz$ to $255Hz$. We find two peaks in the amplitude spectrum, where the left peak appears at the frequency $8Hz$ corresponding to the frequency of the monotone. The amplitude spectrum of the real signal is evenly symmetric about $\\omega=0$, so there is also a peak at the frequency point corresponding to $-8Hz$. After a periodic extension with a sampling rate of $256Hz$, the peak at $-8Hz$ appears at the frequency point corresponding to $256 - 8 = 248 Hz$, i.e. the peak on the right side of the power spectrum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "aly.FFT(input1,256).plot(0, 2*np.pi, xlabel=\"normalized frequency/(rad/s)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we use the normalized frequencies as x-axis, we find that the amplitude spectrum is symmetric about $\\omega=\\pi$. In fact, if we plot the amplitude spectrum of $\\omega\\in (-∞,∞)$, then we can also find that the amplitude spectrum is periodic with $\\omega=2\\pi$ and is evenly symmetric about $\\omega=n\\pi, n\\in \\mathbb Z$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "aly.FFT(input1,256).plot(0, 2*np.pi, plot_type = \"phase\", xlabel=\"normalized frequency/(rad/s)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The phase spectrum of the real signal is also symmetric and also has a period of $\\omega=2\\pi$, but it is oddly symmetric about $\\omega=n\\pi, n\\in \\mathbb Z$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Energy spectrum and power spectrum\n",
    "\n",
    "In addition to the frequency spectrum, **the energy spectrum and the power spectrum** are also functions that can characterize a signal in the frequency domain. The theoretical basis of the energy spectrum and power spectrum is Perceval's theorem, where the signal energy in the time domain is equal to the signal energy in the frequency domain. For finite-energy signals, according to Parseval's theorem, the energy is $E=\\displaystyle\\int_{-∞}^∞x^2(t)dt=\\int_{-∞}^∞|X(j\\omega)|^2d\\omega$, and the energy spectral density is then $G(j\\omega)=|X(j\\omega)|^2$. For a finite-power signal, $x(t)$ is first truncated to a truncated signal of length equal to T $x_T(t),-T/2<t<T/2$ to make it finite-energy. According to Parseval's theorem, its energy is $E=\\displaystyle\\int_{-∞}^{∞}x_T^2(t)dt=\\int_{-∞}^{∞}|X_T(j\\omega)|^2d\\omega$, and the signal power is $P=\\displaystyle\\lim_{T\\rightarrow ∞}\\frac{1}{T}\\int_{-∞}^{∞}|X_T(j\\omega)|^2d\\omega$, then there is a power spectral density $P(j\\omega)=\\displaystyle\\lim_{T\\rightarrow ∞}\\frac{1}{T}|X_T(j \\omega)|^2$.\n",
    "\n",
    "Since we truncate the audio signal by windowing, all signals are finite-energy and finite-power signals. We thus only concerned with their power spectral density, which is calculated as $P[k]=\\frac{1}{N_{max}}|X[k]|^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "input1 = ak.create_Single_Freq_Audio(0.02,8,256,1)\n",
    "aly.PSD(input1, 256).plot(0,32,xlabel=\"frequency/Hz\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The power spectrum can also be expressed in the form of gain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qUh4UNKQgrYmunBYrDCnlq0h5UNCQgrTksVgh0L1GlabdikSbgoYUJNcETKGjYxrKEy4SZQoaUpD8Wxoa0xApBwoaUpDWHBMwheqVJ1ykLChoSEHyScAEEKswaqtiGtMQiTgFDSlIayKZcwKmkBYtFIk+BQ3JWzrteQ+EQ2YwXDk1RKJNQUPyFq4fletihaGGaq10KxJ1ChqSt3wXKwzV16h7SiTqFDQkb/kuVhiqV0tDJPIUNCRv+SZgCtVXV6qlIRJxChqSt3wTMIUaauK0dOiOcJEoU9CQvBU8phFMuT2aqFFEokZBQ/JW8JhGTZy0w5Gu1GBUS0SGgIKG5C0c02go4OY+0Eq3IlGmoCF5C3/p11XH8jovXKtKN/iJRJeChuStNdHFiMoY8Vh+/33U0hCJPgUNyVshS4iAVroVKQclCRpm9u9m9pKZvWBm95vZ6KB8hpkdMbPVweN7WedcYGZ/NbONZvZNM8stObUUXUtHMu/ptnB0tpVyaohEV6laGo8CZ7v7OcDLwK1Z+15x93nB46as8juAG4E5wWPBkNVWjlFoSyMcOFdLQyS6ShI03P0Rdw9/cywHpvV1vJlNBka6+3LPTPK/C3jP4NZSepNvLo1Qd8pX3eAnElnDYUzj48BDWc9nmtkqM3vczC4NyqYCzVnHNAdlUgKZXBr5B41wtpVaGiLRlf83P0dmtgyY1MOu29x9SXDMbUASuDvYtwNodPd9ZnYB8ICZnVXAey8CFgE0NjYWUn3pQ0tHYd1T1fEYVfEKTbkVibBBCxrufkVf+83sBuBq4K1BlxPungASwfZKM3sFeB2wjWO7sKYFZb2992JgMUBTU5PWrCiy1kRhA+GgnBoiUVeq2VMLgC8C73b39qzyCWYWC7ZnkRnw3uTuO4DDZnZRMGvqI8CSElT9pOdeWNa+kHJqiETboLU0+vFtoBp4NJg5uzyYKXUZ8FUz6wLSwE3uvj845zPAj4ERZMZAHjr+RWXwdXSlSaU97/zgIeXUEIm2kgQNd5/dS/l9wH297FsBnD2Y9ZL+tSQyM58KbmlUK0+4SJQNh9lTEiGF5tIINdSopSESZQoakpfuXBoFBo0wp4aIRJOChuSlO5eGBsJFTkoKGpKXlgG3NCrVPSUSYQoakpfuMY0CWxoNNXE6U2kSSWXvE4kiBQ3JSzHGNEA5NUSiSkFD8tIdNAYw5Tb7dUQkWhQ0JC8tHUmqYhVUx/NL9RpSTg2RaFPQkLy0JroKbmXA0fs71NIQiSYFDclLobk0QkdzaihoiESRgobkpdBcGiGNaYhEm4KG5KXQXBqh7jENBQ2RSFLQkLwMJJcGZOUJV/eUSCQpaEheBpJLA6CmsoJYhdGaUJ5wkShS0JC8DHQg3MyUU0MkwhQ0JC8tA2xpgHJqiESZgobkLJFM0ZlMD2hMA5RTQyTKFDQkZ22JzCKDA+meCs/XlFuRaFLQkJwdzaVRWH7wkHJqiESXgobkrDs/eDFaGuqeEomkkgUNM/uamb1gZqvN7BEzmxKUm5l908w2BvvPzzrno2a2IXh8tFR1P1kNNJdGSAPhItFVypbGv7v7Oe4+D/gN8D+D8quAOcFjEXAHgJmNBf4ZmA9cCPyzmY0Z6kqfzAaaSyOkloZIdJUsaLj74ayndYAH2wuBuzxjOTDazCYDVwKPuvt+dz8APAosGNJKn+QGmksjVF8T50hXimQqXYxqicgQGti3f4DM7HbgI8Ah4M1B8VRga9ZhzUFZb+UyRMIcGAOdchu2VNoSKUbValhNJEoG9RtrZsvM7MUeHgsB3P02d58O3A3cUsT3XWRmK8xsxZ49e4r1sie9YrU0GroXLdRSIiJRM6gtDXe/IsdD7wYeJDNmsQ2YnrVvWlC2Dbj8uPLHennfxcBigKamJu/pGMlfa0eSCoMRlYVl7QvVh4sWajBcJHJKOXtqTtbThcBLwfZS4CPBLKqLgEPuvgN4GHi7mY0JBsDfHpTJEAlzaZjZgF5HiZhEoquUYxpfN7PTgTSwBbgpKH8QeAewEWgHPgbg7vvN7GvAs8FxX3X3/UNb5ZNbS0eShgHe2AdHxzQ07VYkekoWNNz9fb2UO3BzL/vuBO4czHpJ71oTXQOebgtHxzTU0hCJHk1dkZwNNJdGSClfRaJLQUNyNtBcGiGNaYhEl4KG5KwlkRzwEiIAdVUa0xCJKgUNyVlrR3GCRqzCqKuKqaUhEkEKGpKzcMptMWSWR9fNfSJRo6AhOUmlnfbOVPeNeQOlREwi0aSgITk5moCpWC2Nyu61rEQkOhQ0JCfhOlEDXaww1KCWhkgklXSVW4mOYi1WGKqvjrPrcEdRXmu4S6edfW2dtHR00dKRDB6Z7cNZZa2JLmqr4kwfW8u0MSOYPqaW6WNHFOUufJFiUdCQfnUm09z1ly0AjK2rKspr1tfE2XGog8df3sNlc8YPeD2r4SaRTPHnjft4eM1Olq3bxd7Wzj6Pr6+OZzIadnTR1pk6Zt+oEZVMHzuCaaMzQWT62FoumzOBGePrBvMSRHqkoCF92nW4g5vvfo4VWw7w8YtncuGMsUV53esvbOSpjXv56J3PcO700Xz2zbN565mnRDp4tHR08dj6PTy8ZiePrd/TPdvs8tMn8IYZYxk5Is7ImkoaaippqIkHj0rqq+PEKjLX7e4cbO9i64F2tu4/QvOB9u7tDbtb+OP63SSSmeRV82eO5QNvmM5VZ09mRNXAVh6W8uHuPLVxHy/tPMwnL51V9Ne3zFJP5aupqclXrFhR6mpE0tOb9nHzz1bR3pnkX993Du86d0pRXz+RTHHfym1897GNNB84wpmTR/LZt8xmwVmTqKgYWPDoSqXZeaiD5gOZX7zbDh6h+cAR9rQkaDp1DAvnTaVxXO2Ar2Fva4JH1+7ikTU7eWrjPjpTacbXV/G2uRN5+1mTeNNp46iOF+8XejrtbDt4hKXPb+cXz27ltf3tNNTEefe5U/jAG6bz+qmjIh14pXDtnUl+/dw2fvLnV9mwu5VJI2t4/IuXF/T/z8xWuntTj/sUNOR47s4Pn9zMvzz0EqeOreV7H76A101sGLT360qlWbJ6O9/940Y27W1jzin13PKW2Vx9zpTuv8B70tLRxea9bWza08amvW0072+n+cARth08wo5DR0hn/dc2g4kNNYwaUcn6XS0AnNc4moXnTuHqc6cwvr4657queu0gT2zYwxMb9vJ880HcYfrYEVw5dxJXnj2J8xvH9FnvYkmnneWb93Hvs1t56MWdJJJpzpjUwHVvmM57zpvK6NridCXK8LZ1fzs/Xb6Fe555jcMdSc6eOpKPvWkm7zxnMjUF5r5R0CiToLGnJcHqrQdZvfUAuw8niMcqiFcY8ZgFP4PnFRXEY0aswpg9oZ6LZ4/PufuiLZHki/e9wG9f2MGVZ03kG9eeO2QDsam089u/7uDbf9jAy7tamTm+jk9ffhoXnDqGzXva2LS3lc1723hlTxub97axpyXRfa4ZTBk1gqmjRzBtTOYxdcwIpo3JDCpPHjWCqnhmsuC2g0f4f89vZ8nq7azbcZhYhXHx7PEsPHcKV5496ZgbGN2dTXvbeHLDXp7YsIe/vLKPts4UsQrj3GmjuOx1E3j73EmcObmhpH/hHzrSxdLV2/jFiq28uO0wVfEKrjxrEtdeMI2LZ48fkiAmQ8fd+cumffz4qVdZtm4XZsaCsyfxsTfN4IJTxwz4/6KCRgSDRkdXijXbD7PqtQNBoDhI84EjAMQrjAkN1STTTjKVDn46qbTTlU5z/EdaU1nBxaeN561nTuStZ57CxJE1Pb7nxt2t3PRfK9m0p5V/XHAGiy6bVZJfhOm088jaXXzrDxtYs/3wMfvG1lUxc3wds8bXMWtCPTPH13HahDoax9UW1Ax/eVcLS1ZvY8nq7TQfOEJ1vIIr5k7k4tPG80LzQZ7YsJdtBzP/7qeOq+XSOeO5ZPYE3njaOEaNGJ6zmtZsP8QvVzRz/6ptHDrSxeRRNVxz/lTed/40Zk2oL3X1pBfuTmcqTWcy8+hKeWY7LEul6Uql2bCrlbv+8iov7WxhTG0lfze/kQ9ddCqTR40oWl0UNCIQNHa3dPD0pv2seHU/q7YeZN2Ow3SlMp/NlFE1nNc4hnnTRzOvcTRnTxnVZ8shHQSPzmSmK+X363axbN3u7l9+50wbxVvPyASQs6aMxMx46K87+MIvn6emMsa3rj+PN80ePyTX3Rd354kNe9ndkmDWhEygGKwuF3fnudcOsGT1dn7zwg72t3XSUBPn4tPGc+nrxnPp7AlFGQMZSolkimVrd/OrlVt5/OU9pB2aTh3D+y+YxjvPmaypvIOkoyvFK3ta2bi7lVd2t/LK3jZaO5Ikkik6utIkkmkSyRSJ7O0gUOTqjEkNfPzimbx73pSCu6D6oqAxDIPGrsMdLN+0j+Wb9vP05n1s2tMGQG1VjHOmjWLe9DGc1zia86aP5pReWgb5cHfW72rh9+t2s2zdLlZvzfTFTx5Vw9zJI/n9S7uZN300d3zo/KL+xRJFXak0W/a1M2NcLfFYedz/uutwB/ev2sYvV2zllT1t1FRWcNXZk3n/BdN446xxVFQY7s6RrhRtiRTtnUnaOzM/w+epNNRVx6ivjlMXTBEOt8Ouv5NJe2eSl3a2sHF36zGPrQfau1v7FQaNY2sZVVtFdbyCmsoY1fGK4BGjuvLodlVQXhWroCpeQWXwsypeQVXMusvG1FZ1/7E3WBQ0ihw0Umlny7421u44zIZdrcQqjNqqGHXV8czPqji11ZmfddUxaqvipNLOyi0HWL5pH09v3s/mvZkg0VAd5w0zx3LRrLHMnzmOs6aMHJJfVHtaEvxx/W5+v24Xz756gKvPmcxt7zyzqDN9ZPhxd1ZvPcivVjaz9PntmRS+1XHS7rR3pU7o2sxVVbwiCCAxzpg0kmvOm8pbzjxlSP4//eaF7fzr715i4blT+djFMxiX46SGQr22r507n9rMvSu20h7cU1MVr2DW+Dpmn1J/zGPm+LpIfqcUNAYQNMK/JtZuP8y6HYdZu+MwL+1o4UhXqv+TezCyJs6FM8d1B4m5U0ZqkFJKoqMrxaNrd/H05n3UxGPUdv/Rk/lDJ/yDJ/xZYUZrIklb8GjpYbulI8nyTfvYdTjBqBGVXH3OZN53wTTOmz56UP4y/t2LO7n5Z88xsaGaHYc7qI5XcP2Fjdx46SymjC5ei9ndWbHlAD98YjMPr91JvMJ41zlTuOr1k5lzSj3Tx9aW1fdYQSPPoNGVSvPffrGatTsOs3lvW/dfXw01ceZOHsmZk0cyd8pI5k4eyZyJ9VSYndCU7/7ZmaI9kSTlzrzpozljkoKElLdU2nlq415+/Vwzv1uzk46uNDPH13HNeVN5z3lTmT62OGNDf3hpF5/66UrOnjqKn35iPrsOd/C9x17h/lXbMIP3njeVm/7mtAEN/nel0jz41x3c+eRmnm8+xOjaSj44v5GPvHFGrxNKysGwCxpm9jVgIZAGdgM3uPt2M7scWAJsDg79tbt/NThnAfB/gRjwA3f/ei7vVWhL4313/JlxdVXMnRIEickjmTZmhG6cEslDS0cXD724k18/18zyTfsBuGjWWK45fxrvOmdKwXeyP7FhD5/4yQpOn9jAf31y/jEz2bYdPML3/7SJnz/zGp2pNO94/WQ+c/lpnDVlVM6vf+hIF/c88xo//vOr7DjUwazxdXz8kpm87/xpJ8Xd98MxaIx098PB9ueAue5+UxA0vuDuVx93fAx4GXgb0Aw8C1zv7mv7e6/hOhAucrLZur+dB1Zt49ertrF5bxuNY2v5+jWvz3um3vJN+7jhR88wY1wd9yy6qNcZdXtbE9z55GZ++pcttCSSvPn0CVzbNB33zP1IbZ1B91pnKuhmy/QOtCaSrNxygPbOFG86bRyfuGQmbz79lAGvUhAlwy5oHFMBs1uBRnf/dB9B443Al939yqxzcPd/6e/1FTREhpdwbaR/WvIim/e2cd0bpnPrO87M6b6XlVv28+EfPsPU0SO4Z9FFOQ16HzrSxX8t38IPn9zM/rYTF46sjBl11fHMBJZgQsucU+q54eIZebVOyklfQaNkCxaa2e3AR4BDwJuzdr3RzJ4HtpMJIGuAqcDWrGOagflDVVcRKR4z45I543no85fyn8te5vt/2sQf1+/mf73n9bxt7sRez3t+60FuuPNZJo2s4e4b5+c8S2rUiEpufvNsPn7xTNbvamFEZYy67tmNJ+d04YEYtH8tM1tmZi/28FgI4O63uft04G7gluC054BT3f1c4FvAAwW+9yIzW2FmK/bs2VOEqxGRYqupjHHrVWfywM0XM6a2ihvvWsFnf76Kfa2JE45ds/0QH/7h04ypq+LuG+dzSkP+g9AjqmLMmz6a0yc1MG1MLWPqqhQwCjAcuqcagQfd/ewe9r0KNAFzUPeUSNnqTKb53uOv8K0/bKC+Os6X330W7z53CmbG+p0tXLf4L9RWxfnFpy5i2pho3ZkfRX11T5UkzJrZnKynC4GXgvJJFkxPMrMLydRvH5mB7zlmNtPMqoDrgKVDW2sRGSxV8Qo+99Y5/PZzl3LquDo+f89qPvmTFfx5414++IPlVMUr+NmN8xUwhoFSjWl83cxOJzPldgtwU1D+fuDTZpYEjgDXeaYplDSzW4CHyUy5vTMY6xCRMvK6iQ3c9+k38aOnNvONR9bz+5d2M76+mp/deBGnjlOmwuGg5N1Tg03dUyLR9Nq+dn745CY+dNGpzBnEfC5yomE5e0pEpC+N42r5ysIThjqlxDR1QEREcqagISIiOVPQEBGRnCloiIhIzhQ0REQkZwoaIiKSMwUNERHJmYKGiIjkrOzvCDezPWSWKinEeGBvEatTCrqG4UHXMDzoGnJzqrtP6GlH2QeNgTCzFb3dSh8VuobhQdcwPOgaBk7dUyIikjMFDRERyZmCRt8Wl7oCRaBrGB50DcODrmGANKYhIiI5U0tDRERypqDRAzNbYGbrzWyjmX2p1PUplJm9amZ/NbPVZhaJTFRmdqeZ7TazF7PKxprZo2a2Ifg5ppR17E8v1/BlM9sWfBarzewdpaxjf8xsupn90czWmtkaM/t8UB6Zz6KPa4jMZ2FmNWb2jJk9H1zDV4LymWb2dPA76hdBGuyhqZO6p45lZjHgZeBtQDOZ/OTXu/vaklasAGb2KtDk7pGZl25mlwGtwF3ufnZQ9m/Afnf/ehDEx7j7P5aynn3p5Rq+DLS6+zdKWbdcmdlkYLK7P2dmDcBK4D3ADUTks+jjGv6WiHwWZmZAnbu3mlkl8CTweeAfgF+7+z1m9j3geXe/YyjqpJbGiS4ENrr7JnfvBO4BFpa4TicNd/8TsP+44oXAT4Ltn5D54g9bvVxDpLj7Dnd/LthuAdYBU4nQZ9HHNUSGZ7QGTyuDhwNvAX4VlA/p56CgcaKpwNas581E7D9aFgceMbOVZrao1JUZgInuviPY3glMLGVlBuAWM3sh6L4att06xzOzGcB5wNNE9LM47hogQp+FmcXMbDWwG3gUeAU46O7J4JAh/R2loFHeLnH384GrgJuDbpNI80x/ahT7VO8ATgPmATuA/yhpbXJkZvXAfcDfu/vh7H1R+Sx6uIZIfRbunnL3ecA0Mj0hZ5SyPgoaJ9oGTM96Pi0oixx33xb83A3cT+Y/XBTtCvqnw37q3SWuT97cfVfw5U8D3ycCn0XQh34fcLe7/zoojtRn0dM1RPGzAHD3g8AfgTcCo80sHuwa0t9RChonehaYE8xOqAKuA5aWuE55M7O6YPAPM6sD3g682PdZw9ZS4KPB9keBJSWsS0HCX7SB9zLMP4tgAPaHwDp3/99ZuyLzWfR2DVH6LMxsgpmNDrZHkJmgs45M8Hh/cNiQfg6aPdWDYAre/wFiwJ3ufntpa5Q/M5tFpnUBEAd+FoXrMLOfA5eTWclzF/DPwAPAvUAjmRWL/9bdh+1Acy/XcDmZ7hAHXgU+lTU2MOyY2SXAE8BfgXRQ/D/IjAlE4rPo4xquJyKfhZmdQ2agO0bmj/x73f2rwff7HmAssAr4kLsnhqROChoiIpIrdU+JiEjOFDRERCRnChoiIpIzBQ0REcmZgoaIiORMQUNOWmb2OTNbZ2Z3l7ouA2Fm15nZbWZ2g5l9+7h9j5lZpHNiy/CioCEns88Ab3P3D4YFWXfZRslVwO9KXQk5OShoyEkpWE56FvCQmR0ys5+a2VPAT4O7cO8zs2eDx8XBOePM7JEgr8EPzGyLmY03sxnH5c74QrAUOmZ2mpn9Llg08gkzOyMo/7GZfdPM/mxmm8zs/Vnn/6Nl8qA8b2ZfD17juaz9c8LnwV3P84Du/b1c77vtaP6I9Wa2uUj/lHKSieJfVSID5u43mdkC4M3ALcC7yCzweMTMfgb8p7s/aWaNwMPAmWTu7H4yuCP3ncAncnirxcBN7r7BzOYD3yWzrDXAZOASMgvQLQV+ZWZXkVl+fL67t5vZWHffHwS2ee6+GvgY8KPgNc4jk0vBM/GDDwR3QodmB9e7NHgPzOxe4PE8/8lEAAUNkdBSdz8SbF8BzA1+CQOMDFZKvQy4BsDdf2tmB/p6weCcNwG/zHqt6qxDHggWzVtrZuES41cAP3L39uB9wiU6fgB8zMz+AfgARxfZWwA8lPWav3D3W7Lq8NhxdfoicMTdv9NX3UV6o6AhktGWtV0BXOTuHdkHZP3iP16SY7t6a7Je52CwrHVPstcK6vXFA/eRaen8AVjp7vuC8rcD7+vn3MwbmF0BXEsm+IkURGMaIid6BPhs+MTM5gWbfwL+Lii7CgiT9+wCTgnGPKqBqwGC3A2bzeza4Bwzs3P7ee9HybQoaoNzxgav1UGmm+wOgq4pMxsFxLMCSK/M7FTgO8C1WS0qkbwpaIic6HNAk2Uyu60FbgrKvwJcZmZryHRTvQbg7l3AV4FnyPzSfynrtT4IfMLMngfW0E/qYHf/HZmxhxWWydb2hazdd5NZrfWR4PnbgGU5XtMNwDjggWAw/MEczxM5hla5FSmQmb0KNLn73iF6vy8Ao9z9n4LnPwB+4O7Lh+L9RUBjGiKRYGb3k0lRGs68wt0/WboayclKLQ0REcmZxjRERCRnChoiIpIzBQ0REcmZgoaIiORMQUNERHKmoCEiIjn7/4S1HDBPeRemAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.PSD(input1, 256, dB=True).plot(0,32,xlabel=\"frequency/Hz\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When there are two frequency components in the signal at the same time, the power information of both of them will be reflected in the power spectrum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "input2 = ak.create_Single_Freq_Audio(0.01,24,256,1)\n",
    "aly.PSD(input1 + input2, 256).plot(0,32,xlabel=\"frequency/Hz\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The power spectral density on $16Hz$ is a quarter of that on $8Hz$ since the amplitude of input2 is half that of input1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Frequency domain characteristics of noise\n",
    "\n",
    "Unlike deterministic periodic signals and musical tones with distinct pitches, noise has no distinct pitch, i.e., no distinct periodicity. While musical tones can show distinct peaks in the amplitude and power spectrum, the frequency components of noise show a continuous and random distribution.\n",
    "\n",
    "The frequency components of white noise are uniformly distributed over the entire frequency range."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(None, None)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "monotone_without_wn = ak.create_Single_Freq_Audio(0.02,440,44100,1)\n",
    "monotone_with_wn = monotone_without_wn.addWgn(10)   #Add Gaussian white noise with a signal-to-noise ratio of 10 dB to a monotone\n",
    "wn = monotone_with_wn - monotone_without_wn #Subtract monotone, leaving only white noise\n",
    "aly.FFT(wn).plot(), aly.PSD(wn).plot()"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "34e3d493db18dfecee561d26c028e75a8172bde10b9fb1f75764229aafdf7eef"
  },
  "kernelspec": {
   "display_name": "Python 3.8.3 ('base')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
